CBSE Class 11 Physics Unit And Measurement Worksheet

Question. Random error can be eliminated by
(a) careful observation
(b) eliminating the cause
(c) measuring the quantity with more than one instrument
(d) taking large number of observations and then their mean.

Answer: D

Question. Electron volt is a unit of
(a) potential difference
(b) charge
(c) energy
(d) capacity

Answer: C

Question. Which of the following systems of units is not based on units of mass, length and time alone
(a) SI
(b) MKS
(b) CGS
(d) FPS

Answer: A

Question. The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure difference across the ends)n and (average velocity of the liquid)m. Which of the following relations between m and n is correct?
(a) m = n
(b) m = – n
(c) m² = n
(d) m = – n²

Answer: B

Question. Unit of latent heat is
(a) J Kg^–1
(b) J mol^–1
(c) N Kg^–1
(d) N mol^–1

Answer: A

Question. Dyne-sec is the unit of
(a) momentum
(b) force
(c) work
(d) angular momentum

Answer: A

Question. The expression [ML^–1 T^–2] does not represent
(a) pressure
(b) power
(c) stress
(d) Young’s modulus

Answer: B

Question. Temperature can be expressed as derived quantity in terms of
(a) length and mass
(b) mass and time
(c) length, mass and time
(d) None of these

Answer: D

Question. The SI unit of coefficient of mutual inductance of a coil is
(a) henry
(b) volt
(c) farad
(c) weber

Answer: A

Question. Light year is
(a) light emitted by the sun in one year.
(b) time taken by light to travel from sun to earth.
(c) the distance travelled by light in free space in one year.
(d) time taken by earth to go once around the sun.

Answer: C

Question. The SI unit of pressure is
(a) atmosphere
(b) bar
(c) pascal
(d) mm of Hg

Answer: C

Question. If e is the charge, V the potential difference, T the temperature then the units of eV/T are the same as that of
(a) Planck’s constant
(b) Stefan’s constant
(c) Boltzmann constant
(d) gravitational constant

Answer: C

Question. Which physical quantities have same dimensions?
(a) Moment of couple and work
(b) Force and power
(c) Latent heat and specific heat
(d) Work and power

Answer: A

Question. Dimensions of impulse are
(a) [MLT^-1]
(b) [MLT₂ ]
(c) [MT^-2 ]
(d) [ML^-1T^-3 ]

Answer: A

Question. N kg^-1 is the unit of
(a) velocity
(b) force
(c) acceleration
(d) None of these

Answer: C

Question. Two quantities A and B have different dimensions which mathematical operation given below is physically meaningful?
(a) A/B
(b) A + B
(c) A – B
(d) A = B

Answer: A

Question. The S.I. unit of pole strength is
(a) Am²
(b) Am
(c) A m^–1
(d) Am^–2

Answer: B

Question. What is the unit of “a” in Vander Waal’s gas equation?
(a) Atm litre^–2 mol²
(b) Atm litre² per mol
(c) Atm litre^–1 mol²
(d) Atm litre² mol^–2

Answer: B

Question. Illuminance of a surface is measured in
(a) Lumen
(b) candela
(c) lux
(d) lux m^–2

Answer: C

Question. Potential is measured in
(a) joule/coulomb
(b) watt/coulomb
(c) newton-second
(d) None of these

Answer: A

Question. If f = x², then the relative error in f is
(a) 2Δx/x
(b) (Δx)²/x
(c) Δx/x
(d) (Δx)²

Answer: A

Question. Maxwell is the unit of
(a) magnetic susceptibility
(b) intensity of Magnetisation
(c) magnetic Flux
(d) magnetic Permeability

Answer: C

Question. SI unit of electric polarisation is
(a) Cm^–2
(b) coulomb
(c) ampere
(d) volt

Answer: A

Question. Which is dimensionless?
(a) Force/acceleration
(b) Velocity/acceleration
(c) Volume/area
(d) Energy/work

Answer: D

Question. Which of the following is a derived physical quantity?
(a) Mass
(b) Velocity
(c) Length
(d) Time

Answer: B

Question. The dimensions of Rydberg’s constant are
(a) [M⁰ L^–1 T]
(b) [MLT^–1]
(c) [M⁰ L^–1 T⁰]
(d) [ML⁰ T^2]

Answer: C

Question. The velocity of a body which falls under gravity varies as ga hb, where g is acc. due to gravity and h is the height. The values of a and b are
(a) a = 1, b = 1/2
(b) a = b = 1
(c) a = 1/2, b = 1
(d) a = 1/2; b = 1/2

Answer: D

Question. The dimensions of a rectangular block measured with callipers having least count of 0.01 cm are 5 mm × 10 mm × 5 mm. The maximum percentage error in the measurement of the volume of the block is
(a) 5%
(b) 10%
(c) 15%
(d) 20%

Answer: A

Question. The dimensions of Wien’s constant are
(a) [ML⁰ T K]
(b) [M⁰ LT⁰ K]
(c) [M⁰ L⁰ T K]
(d) [MLTK]

Answer: B

Question. What are the units of magnetic permeability?
(a) Wb A^–1 m^–1
(b) Wb^–1 Am
(c) Wb A m^–1
(d) Wb A^–1 m

Answer: A

Question. What is the fractional error in g calculated from T = 2π√l / g ? Given fraction errors in T and l are ± x and ± y respectively.
(a) x + y
(b) x – y
(c) 2x + y
(d) 2x – y

Answer: C

Question. Using mass (M), length(L), time (T) and electric current (A) as fundamental quantities the dimensions of permittivity will be
(a) [MLT^–1A^–1]
(b) [MLT^–2A^–2]
(c) [M^–1L^–3T⁺⁴A²]
(d) [M²L^–2T^–2A²]

Answer: C

Question. Distance travelled by a particle at any instant ‘t’ can be represented as S = A (t + B) + Ct². The dimensions of B are
(a) [M⁰ L¹T^-1]
(b) [M⁰ L⁰ T¹]
(c) [M⁰ L^-1T^-2 ]
(d) [M⁰ L² T^-2]

Answer: B

Question. The deBroglie wavelength associated with a particle of mass m and energy E is h /√2mE . The dimensional formula of Planck’s constant h is
(a) [M² L² T^-2 ]
(b) [ML² T^-1]
(c) [MLT^-2 ]
(d) [ML² T^-2 ]

Answer: B

Question. Consider the following pairs of quantities
1. Young's modulus; pressure
2. Torque; energy
3. Linear momentum; work
4. Solar day; light year.
In which cases are the dimensions, within a pair, same?
(a) 1 and 3
(b) 1 and 4
(c) 1 and 2
(d) 2 and 4

Answer: C

Question. The velocity v of a particle at time t is given by v = at + b/t+c The dimensions of a, b c are respectively
(a) [LT^–2], [L], [T]
(b) [L2], [T] and [LT²]
(c) [LT²], [LT] and [L]
(d) [L], [LT] and [T²]

Answer: A

Question. The dimensions of Hubble’s constant are
(a) [T^-1]
(b) [M⁰L⁰T^-2 ]
(c) [MLT⁴ ]
(d) [MT^-1 ]

Answer: A

Question. When 97.52 is divided by 2.54, the correct result is
(a) 38.3937
(b) 38.394
(c) 38.39
(d) 38.4

Answer: D

Question. The dimensional formula for relative density is
(a) [M L^–3]
(b) [M⁰ L^–3]
(c) [M⁰ L⁰ T^–1]
(d) [M⁰ L⁰ T⁰]

Answer: D

Question. If L denotes the inductance of an inductor through which a current i is flowing, the dimensions of Li² are
(a) [ML² T^–2]
(b) [MLT^–2]
(c) [M² L² T^–2]
(d) Not expressible in M, L, T

Answer: A

Question. In a Vernier calliper, N divisions of vernier scale coincide with (N–1) divisions of main scale (in which one division represents 1 mm). the least count of the instrument in cm. should be
(a) N
(b) N – 1
(c) 1/10N
(d) 1/N -1

Answer: C

Question. Error in the measurement of radius of a sphere is 1%. Then error in the measurement of volume is
(a) 1%
(b) 5%
(c) 3%
(d) 8%

Answer: C

Question. The dimensional formula of couple is
(a) [ML²T^-2 ]
(b) [MLT² ]
(c) [ML^-1T^-3 ]
(d) [ML^-2T^-2]

Answer: A

Question. Relative density of a metal may be found with the help of spring balance. In air the spring balance reads (5.00 ± 0.05) N and in water it reads (4.00 ± 0.05) N. Relative density would be
(a) (5.00 ± 0.05)N
(b) (5.00 ± 11%)
(c) (5.00 ± 0.10)
(d) (5.00 ± 6%)

Answer: D

Question. Area of a square is (100 ± 2) m². Its side is
(a) (10 ± 1) m (b)
(10 ± 0.1) m
(c) (10 ±√2)m
(d) 10 ±√2%

Answer: A

Question. The percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error, in kinetic energy obtained by measuring mass and speed, will be
(a) 12 %
(b) 10 %
(c) 8 %
(d) 2 %

Answer: C

Question. The potential energy of a particle varies with distance x from a fixed origin as V = A√x/ x + B where A and B are constants.
The dimensions of AB are
(a) [M¹L^{5/ 2} T^-2 ]
(b) [M¹L² T^-2 ]
(c) [M^3/2 L^{5/ 2} T^-2 ]
(d) [M¹L⁷/ 2 T^-2 ]

Answer: D

Question. Let Q denote the charge on the plate of a capacitor of capacitance C. The dimensional formula for Q2/C is
(a) [L²M²T]
(b) [LMT² ]
(c) [L²MT^-2 ]
(d) [L²M²T² ]

Answer: C

Question. If L and R denote inductance and resistance then dimension of L/R is
(a) [M⁰L⁰T⁰ ]
(b) [M⁰L⁰T]
(c) [M²L⁰T² ]
(d) [MLT² ]

Answer: B

Question. The dimensional formula of current density is
(a) [M⁰L-2T^-1Q]
(b) [M⁰L²T1Q^-1]
(c) [MLT^-1Q]
(d) [ML^-2T^-1Q² ]

Answer: A

Question. The period of a body under S.H.M. is represented by: T = P^a D^b S^c where P is pressure, D is density and S is surface tension, then values of a, b and c are
(a) -3/2 , 1/2 , 1
(b) -1, - 2, 3
(c) 1/2 , -3/2 , -1/2
(d) 1, 2 1/3

Answer: A

Question. The least count of a stop watch is 0.2 second. The time of 20 oscillations of a pendulum is measured to be 25 second.
The percentage error in the measurement of time will be
(a) 8%
(b) 1.8%
(c) 0.8%
(d) 0.1%

Answer: C

Question. Multiply 107.88 by 0.610 and express the result with correct number of significant figures.
(a) 65.8068
(b) 65.807
(c) 65.81
(d) 65.8

Answer: D

Question. The dimensions of universal gas constant are
(a) [L² M¹ T^–2 K^–1]
(b) [L¹ M² T^–2 K^–1]
(c) [L¹ M¹ T^–2 K^–1]
(d) [L² M² T^–2 K^–1]

Answer: A

Question. Dimensions of specific heat are
(a) [ML² T^–2 K]
(b) [ML² T^–2 K^–1]
(c) [ML² T² K^–1]
(d) [L² T^–2 K^–1]

Answer: D

Question. The dimensional formula of wave number is
(a) [M0 L⁰ T^–1]
(b) [M⁰ L^–1 T⁰]
(c) [M^–1 L^–1 T⁰]
(d) [M⁰ L⁰ T⁰]

Answer: B

Question. Which of the following is the most accurate?
(a) 200.0 m
(b) 20 × 101 m
(c) 2 × 10² m
(d) data is inadequate

Answer: A

Question. Density of liquid is 16.8 g cm^–3. Its value in the International System of Units is
(a) 16.8 kgm^-3
(b) 168 kgm^-3
(c) 1680 kgm^-3
(d) 16800 kgm-3

Answer: D

Question. Subtract 0.2 J from 7.26 J and express the result with correct number of significant figures.
(a) 7.1 J
(b) 7.06 J
(c) 7.0 J
(d) 7 J

Answer: A

Question. The pressure on a square plate is measured by measuring the force on the plate and length of the sides of the plate by using the formula P = F/l2. If the maximum errors in the measurement of force and length are 4% and 2% respectively, then the maximum error in the measurement of pressure is
(a) 1%
(b) 2%
(c) 8%
(d) 10%

Answer: C

Question. The Richardson equation is given by I = AT²e^–B/kT. The dimensional formula for AB² is same as that for
(a) I T²
(b) kT
(c) I k²
(d) I k²/T

Answer: C

Question. If C and L denote the capacitance and inductance, the dimensions of LC are
(a) [M⁰ L⁰ T^–1]
(b) [M⁰ L^–1 T⁰]
(c) [M^–1 L^–1 T⁰]
(d) [M⁰ L⁰ T²]

Answer: D

Question. The refractive index of water measured by the relation µ = real depth/apparent depth is found to have values of 1.34, 1.38, 1.32 and 1.36; the mean value of refractive index with percentage error is
(a) 1.35 ± 1.48 %
(b) 1.35 ± 0 %
(c) 1.36 ± 6 %
(d) 1.36 ± 0 %

Answer: A

Question. Which of the following is the unit of molar gas constant?
(a) JK^–1 mol^–1
(b) Joule
(c) JK^–1
(d) J mol^–1

Answer: A

Question. The dimensions of solar constant is
(a) [M⁰ L⁰ T⁰]
(b) [MLT^–2]
(c) [ML² T^–2]
(d) MT^–3

Answer: D

Question. The dimensions of 1/∈_º e²/hc are 
(a) M^–1 L^–3 T⁴ A²
(b) ML3 T^–4 A^–2
(c) M⁰ L⁰ T⁰ A⁰
(d) M^–1 L^–3 T² A

Answer: C

Question. The unit of current in C.G..S. system is
(a) 10 A
(b) 1/10 A
(c) 1/100 A
(d) 1/1000 A

Answer: C

Question. The dimensions of pressure gradient are
(a) [ML^–2 T^–2]
(b) [ML^–2 T^–1]
(c) [ML^–1 T^–1]
(d) [ML–1 T^–2]

Answer: A

Question. A quantity is represented by X = M^a L^b T^c. The % error in measurement of M, L and T are α%, β% and γ% respectively. The % error in X would be
(a) (αa +βb + γ c)%
(b) (αa -vb + γ c)%
(c) (αa -βb - γ c) x100%
(d) None of these

Answer: A

Question. Conversion of 1 MW power in a New system of units having basic units of mass, length and time as 10 kg, 1 dm and 1 minute respectively is
(a) 2.16 × 10¹⁰ unit
(b) 2 × 10⁴ unit
(c) 2.16 × 10¹² unit
(d) 1.26 × 10¹² unit

Answer: C

Question. In the equation X = 3YZ², X and Z are dimensions of capacitance and magnetic induction respectively. In MKSQ system, the dimensional formula for Y is
(a) [M^–3 L^–2 T^–2 Q^–4]
(b) [M L^–2]
(c) [M^–3 L^–2 Q⁴ T⁸]
(d) [M^–3 L^–2 Q⁴ T⁴]

Answer: D

Question. Suppose the kinetic energy of a body oscillating with amplitude A and at a distance x is given by
K = Bx/x² + A²
The dimensions of B are the same as that of
(a) work/time
(b) work × distance
(c) work/distance
(d) work × time

Answer: B

Question. A resistor of 10 k Ω having tolerance 10% is connected in series with another resistor of 20 k Ω having tolerance 20%.
The tolerance of the combination will be
(a) 10%
(b) 13%
(c) 30%
(d) 20%

Answer: C

Question. In the eqn. (P + a/V²) (V-b)=constant, the unit of a is
(a) dyne × cm⁵
(b) dyne × cm⁴
(c) dyne/cm³
(d) dyne × cm²

Answer: B

Question. Dimensions of ‘ohm’ are same as (where h is Planck’s constant and e is charge)
(a) h/e
(b) h²/e
(c) h/e²
(d) h²/e²

Answer: C

Question. The dimensions of magnetic moment are
(a) [L² A¹]
(b) [L² A^–1]
(c) [L² / A³]
(d) [LA²]

Answer: A

Question. The solid angle sustended by the total surface area of a sphere, at the centre is
(a) 4p
(b) 2p
(c) p
(d) 3p

Answer: A

Question. The dimensional formula for entropy is
(a) [MLT^–2 K¹]
(b) [ML² T^–2]
(c) [ML² T^–2 K^–1]
(d) [ML² T^–2 K]

Answer: C

Question. Two full turns of the circular scale of a screw gauge cover a distance of 1mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of – 0.03 mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circulr scale divisions in line with the main scale as 35. The diameter of the wire is
(a) 3.32 mm
(b) 3.73 mm
(c) 3.67 mm
(d) 3.38 mm

Answer: D

Question. The unit and dimensions of impedance in terms of charge Q are
(a) mho, [ML² T^–2 Q^–2]
(b) ohm, [ML² T^–1 Q^–2]
(c) ohm, [ML² T^–2 Q^–1]
(d) ohm, [MLT^–1 Q^–1]

Answer: B

Question. L, C, R represent physical quantities inductance, capacitance and resistance respectively. The combinations which have the dimensions of frequency are
(a) 1/RC
(b) R/L
(c) 1/ LC
(d) C/L

Answer: C

Question. The time of oscillation T of a small drop of liquid depends on radius r, density r and surface tension S. The relation between them is given by

Answer: B

Question. If I is the moment of inertia and ω the angular velocity, what is the dimensional formula of rotational kinetic energy 1/2Iω2 ?
(a) [ML²T^-1]
(b) [M²L^-1T^-2 ]
(c) [ML²T^-2 ]
(d) [M²L^-1T^-2 ]

Answer: C

Question. Given that r = m² sin πt , where t represents time. If the unit of m is N, then the unit of r is
(a) N
(b) N²
(c) Ns
(d) N²s

Answer: B

Question. The dimensional formula of farad is
(a) [M^-1L^-2TQ]
(b) [M^-1L^-2T²Q² ]
(c) [M^-1L^-2TQ² ]
(d) [M^-1L^-2T²Q]

Answer: B

Question. The velocity of water waves (v) may depend on their wavelength l, the density of water r and the acceleration due to gravity, g. The method of dimensions gives the relation between these quantities is
(a) v
(b) v² ∝gλ
(c) v² ∝g λ²
(d) v² ∝g-1 λ²

Answer: B

Question. Turpentine oil is flowing through a capillary tube of length l and radius r. The pressure difference between the two ends of the tube is p. The viscosity of oil is given by :
η = p(r² - x²)/4vl . Here v is velocity of oil at a distance x from the axis of the tube. From this relation, the dimensional formula of η is
(a) [ML^-1T^-1]
(b) [MLT -1]
(c) [ML²T^-2 ]
(d) [M⁰L⁰T⁰ ]

Answer: A

Question. The dimensional formula of velocity gradient is
(a) [M⁰L⁰T^-1]
(b) [MLT¹]
(c) [ML⁰T^-1]
(d) [M⁰LT^-2 ]

Answer: A

Question. The thrust developed by a rocket-motor is given by F = mv + A(P₁ - P₂ ) where m is the mass of the gas ejected per unit time, v is velocity of the gas, A is area of crosssection of the nozzle, P₁ and P₂ are the pressures of the exhaust gas and surrounding atmosphere. The formula is dimensionally
(a) correct
(b) wrong
(c) sometimes wrong, sometimes correct
(d) Data is not adequate

Answer: A

Question. The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are 4% and 3% respectively, the maximum error in the measurement of density will be
(a) 7%
(b) 9%
(c) 12%
(d) 13%

Answer: D

Question. The speed of sound in a gas is given by v = √γRT/M 
R = universal gas constant,
T = temperature
M = molar mass of gas
The dimensional formula of g is
(a) [M⁰L⁰T⁰ ]
(b) [M⁰LT^-1]
(c) [MLT^-2 ]
(d) [M⁰L⁰T^-1]

Answer: A

Question. A cube has numerically equal volume and surface area. The volume of such a cube is
(a) 1000 unit
(b) 200 unit
(c) 216 unit
(d) 300 unit

Answer: C

Question. The time of reverberation of a room A is one second. What will be the time (in seconds) of reverberation of a room, having all the dimensions double of those of room A?
(a) 2
(b) 4
(c) 1/2
(d) 1

Answer: A

Question. The physical quantity which has the dimensional formula [M¹T^–3] is
(a) surface tension
(b) solar constant
(c) density
(d) compressibility

Answer: B

Question. Specific gravity has ............ dimensions in mass, ............ dimensions in length and ............ dimensions in time.
(a) 0, 0, 0
(b) 0, 1, 0
(c) 1, 0, 0
(d) 1, 1, 3

Answer: A

Question. The dimensions of magnetic field in M, L, T and C (coulomb) are given as
(a) [MLT^–1 C^–1]
(b) [MT² C^–2]
(c) [MT^–1 C^–1]
(d) [MT^–2 C^–1]

Answer: C

Question. In a simple pendulum experiment for the determination of acceleration due to gravity, time period is measured with an accuracy of 0.2% while length was measured with an accuracy of 0.5%. The percentage accuracy in the value of g so obtained is
(a) 0.25%
(b) 0.7%
(c) 0.9%
(d) 1.0%

Answer: C

Question. Which of the following do not have the same dimensional formula as the velocity?
Given that μ0 = permeability of free space, ε0 = permittivity
of free space, ν = frequency, λ = wavelength, P = pressure, ρ
= density, ω = angular frequency, k = wave number,
(a) 1/√μ0 ε0
(b) νλ
(c) √P/ρ
(d) ωk

Answer: D

Question. A vernier calliper has 20 divisions on the vernier scale, which coincide with 19 on the main scale. The least count of the instrument is 0.1 mm. The main scale divisions are of
(a) 0.5 mm
(b) 1 mm
(c) 2 mm
(d) 1/4 mm

Answer: C

Question. The time dependence of a physical quantity p is given by p = p₀ exp. (– α t²), where a is a constant and t is the time.
The constant a
(a) is dimensionless
(b) has dimensions T^–2
(c) has dimensions T²
(d) has dimensions of p.

Answer: B

Question. If time T, acceleration A and force F are regarded as base units, then the dimensional formula of work is
(a) [FA]
(b) [FAT]
(c) [FAT² ]
(d) [FA2T]

Answer: C

Question. The pitch of the screw gauge is 0.5 mm. Its circular scale contains 50 divisions. The least count of the screw gauge is
(a) 0.001 mm
(b) 0.01 mm
(c) 0.02 mm
(d) 0.025 mm

Answer: B

Question. The equation of a wave is given by y = a sin ω(x/v - k) , where ω is angular velocity and v is linear velocity. The dimensions of K will be
(a) [T²]
(b) [T^–1]
(c) [T]
(d) [L T]

Answer: C

Question. The physical quantity having the dimensions [M^–1L^–3T³A²] is
(a) resistance
(b) resistivity
(c) electrical conductivity
(d) electromotive force

Answer: C

Question. If the dimensions of a physical quantity are given by Ma Lb Tc, then the physical quantity will be
(a) velocity if a = 1, b = 0, c = – 1
(b) acceleration if a = 1, b = 1, c = – 2
(c) force if a = 0, b = – 1, c = – 2
(d) pressure if a = 1, b = – 1, c = – 2

Answer: D

Question. If E, m, J and G represent energy, mass, angular momentum and gravitational constant respectively, then the dimensional formula of EJ² /m⁵G² is
(a) angle
(b) length
(c) mass
(d) time

Answer: A

Question. What is the fractional error in g calculated from T = 2π√l /g ? Given fractional errors in T and l are ± x and ± y respectively.
(a) x + y
(b) x – y
(c) 2x + y
(d) 2x – y

Answer: C

Question. A force is given by F = at + bt², where t is time, the dimensions of a and b are
(a) [M L T^–4] and [M L T^–1]
(b) [M L T^–1] and [M L T⁰]
(c) [M L T^–3] and [M L T^–4]
(d) [M L T^–3] and [M L T⁰]

Answer: C

Question. Which one of the following has the same dimension as that of time, if R is resistance, L inductance and C is capacitance?
(a) RC
(b) √LC
(c) L/R
(d) All of the above

Answer: B

Question. The dimensions of voltage in terms of mass (M), length (L) and time (T) and ampere (A) are
(a) [ML²T^–2A^–2]
(b) [ML²T³A^–1]
(c) [ML²T^–3A¹]
(d) [ML²T–3A^–1]

Answer: D

Question. The resistance R of a wire is given by the relation R = ρlπr2. Percentage error in the measurement of r, l and r is 1%, 2% and 3% respectively. Then the percentage error in the measurement of R is :
(a) 6
(b) 9
(c) 8
(d) 10

Answer: B

Question. The heat generated in a circuit is given by Q = I² Rt, where I is current, R is resistance and t is time. If the percentage errors in measuring I, R and t are 2%, 1% and 1% respectively, then the maximum error in measuring heat will be
(a) 2%
(b) 3%
(c) 4%
(d) 6%

Answer: D

Question. The density of a material in CGS system of units is 4g/cm³. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be
(a) 0.4
(b) 40
(c) 400
(d) 0.04

Answer: B

Question. What are the dimensions of permeability ?
(a) [M¹L¹T¹A^–2]
(b) [M¹L¹T^–2A^–2]
(c) [M²L²T¹A⁰]
(d) [M¹L²T²A^–2]

Answer: B

Question. In a vernier callipers, ten smallest divisions of the vernier scale are equal to nine smallest division on the main scale. If the smallest division on the main scale is half millimeter, then the vernier constant is
(a) 0.5 mm
(b) 0.1 mm
(c) 0.05 mm
(d) 0.005 mm

Answer: C

Question. The frequency of vibration of a string is given by f = n/2L √T/m , where T is tension in the string, L is the length, n is number of harmonics. The dimensional formula for m is
(a) [M⁰ L T]
(b) [M¹ L^–1 T^–1]
(c) [M¹ L^–1 T⁰]
(d) [M⁰ L T^–1]

Answer: C

Question. Diameter of a steel ball is measured using a Vernier callipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given below: 

If the zero error is – 0.03 cm, then mean corrected diameter is
(a) 0.52 cm
(b) 0.59 cm
(c) 0.56 cm
(d) 0.53 cm

Answer: B

Question. In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively.
Quantity P is calculated as follows
P = a³b³/cd % error in P is
(a) 10%
(b) 7%
(c) 4%
(d) 14%

Answer: D

Question. The period of oscillation of a simple pendulum is T = 2π√L/g. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1s resolution. The accuracy in the determination of g is
(a) 1%
(b) 5%
(c) 2%
(d) 3%

Answer: D

Each question contains
STATEMENT-1 and STATEMENT-2. Choose the correct answer
(ONLY ONE option is correct ) from the following
(a) Statement -1 is false, Statement-2 is true
(b) Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
(c) Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
(d) Statement -1 is true, Statement-2 is false

Question. Statement 1 : In the measurement of physical quantities direct and indirect methods are used.
Statement 2 : The accuracy and precision of measuring instruments along with errors in measurements should be taken into account, while expressing the result.

Answer: B

Question. Statement 1 : Energy cannot be divided by volume.
Statement 2 : Because dimensions for energy and volume are different.

Answer: A

Question. Statement 1 : The number of significant figures depends on the least count of measuring instrument.
Statement 2 : Significant figures define the accuracy of measuring instrument.

Answer: C

Question. Statement 1 : Absolute error may be negative or positive.
Statement 2 : Absolute error is the difference between the real value and the measured value of a physical quantity.

Answer: B

Question. The mass and volume of a body are 4.237 g and 2.5 cm³, respectively. The density of the material of the body in correct significant figures is
(a) 1.6048 g cm^–3
(b) 1.69 g cm^–3
(c) 1.7 g cm^–3
(d) 1.695 g cm^–3

Answer: C

Question. If dimensions of critical velocity ucof a liquid flowing through a tube are expressed as [η^xρ^yr^x ] , where h, r and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by : 
(a) –1, –1, 1
(b) –1, –1, –1
(c) 1, 1, 1
(d) 1, –1, –1

Answer: D

Question. Measure of two quantities along with the precision of respective measuring instrument is
A = 2.5 ms–1 ± 0.5 ms^–1,
B = 0.10 s ± 0.01 s. The value of AB will be
(a) (0.25 ± 0.08) m
(b) (0.25 ± 0.5) m
(c) (0.25 ± 0.05) m
(d) (0.25 ± 0.135) m

Answer: A

Question. The numbers 2.745 and 2.735 on rounding off to 3 significant figures will give
(a) 2.75 and 2.74
(b) 2.74 and 2.73
(c) 2.75 and 2.73
(d) 2.74 and 2.74

Answer: D

Question. If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be : 
(a) [EV^–1T^–2]
(b) [EV^–2T^–2]
(c) [E^–2V^–1T^–3]
(d) [EV^–2T^–1]

Answer: B

Question. You measure two quantities as A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m. We should report correct value for √AB as
(a) 1.4 m ± 0.4 m
(b) 1.41 m ± 0.15 m
(c) 1.4 m ± 0.3 m
(d) 1.4 m ± 0.2 m

Answer: D

Question. Which of the following measurement is most precise?
(a) 5.00 mm
(b) 5.00 cm
(c) 5.00 m
(d) 5.00 km

Answer: A

Question. The number of significant figures in 0.06900 is
(a) 5
(b) 4
(c) 2
(d) 3

Answer: B

Question. Young's modulus of steel is 1.9 × 1011 N/m². When expressed in CGS units of dyne/cm², it will be equal to (1N = 10⁵ dyne, 1 m² = 10⁴ cm²)
(a) 1.9 × 10¹⁰
(b) 1.9 × 10¹¹
(c) 1.9 × 10¹²
(d) 1.9 × 10¹³

Answer: C

Question. The length and breadth of a rectangular sheet are 16.2 ± 0.1 cm and 10.1 ± 0.1 cm, respectively. The area of the sheet in appropriate significant figures and error is
(a) 164 ± 3 cm²
(b) 163.62 ± 2.6 cm²
(c) 163.6 ± 2.6 cm²
(d) 163.62 ± 3 cm²

Answer: A

Question. In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively.
Quantity P is calculated as follows P = a³b²/cd % error in P is:
(a) 10%
(b) 7% 
(c) 4%
(d) 14%

Answer: D

Question. The pair of quantities having same dimensions is
(a) Young’s modulus and energy
(b) impulse and surface tension
(c) angular momentum and work
(d) work and torque

Answer: D

Question. The sum of the numbers 436.32, 227.2 and 0.301 in appropriate significant figures is
(a) 663.821
(b) 664
(c) 663.8
(d) 663.82

Answer: B

Question. The mean length of an object is 5 cm. Which is the following measurement is most accurate?
(a) 4.9 cm
(b) 4.805 cm
(c) 5.25 cm
(d) 5.4 cm

Answer: A

Question. Which of the following pairs of physical quantities does not have same dimensional forrmula?
(a) Work and torque
(b) Angular momentum and Planck's constant
(c) Tension and surface tension
(d) Impulse and linear momentum

Answer: C

Question. If momentum (p), area (A) and time (T) are taken to be fundamental quantities, then energy has the dimensional formula
(a) [pA^–1T¹]
(b) [p²AT]
(c) [pA^–1/2T]
(d) [ pA^1/2T]

Answer: D

Question. If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are :
(a) [F V T^–1]
(b) [F V T^–2]
(c) [F V^–1 T^–1]
(d) [F V^–1 T]

Answer: D