CBSE Class 11 System of particles and Rotational Motion Worksheet A

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Question. A particle of mass m is moving in yz-plane with a uniform velocity v with its trajectory running parallel to +ve y-axis and intersecting z-axis at z = a in figure. The change in its angular momentum about the origin as it bounces elastically from a wall at y = constant is
(a) mvae̅_x
(b) 2mvae̅_x
(c) ymve̅_x
(d) 2ymve̅x

Answer: B

Question. A small object of uniform density rolls up a curved surface with an initial velocity ‘n’. It reaches upto a maximum height of 3v2/4g with respect to the initial position. The object is a
(a) solid sphere
(b) hollow sphere 
(c) disc
(d) ring

Answer: C

Question. Point masses m₁ and m₂ are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity w0 is minimum, is given by :

Answer: C

Question. In problem-5, the CM of the plate is now in the following quadrant of x-y plane.
(a) I
(b) II
(c) III
(d) IV

Answer: C

Question. A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ? 
(a) 0.25 rad/s²
(b) 25 rad/s²
(c) 5 m/s²
(d) 25 m/s²

Answer: B

Question. A rod of weight W is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance d from each other. The centre of mass of the rod is at distance x from A. The normal reaction on A is
(a) Wd/x
(b) W(d-x)/x
(c) W(d-x)/d
(d) Wx/d

Answer: C

Question. The density of a non-uniform rod of length 1 m is given by r(x) = a (1 + bx²) where, a and b are constants and 0 ≤ x ≤.The centre of mass of the rod will be at
(a) 3(2+b)/4(3+b)
(b) 4(2+b)/3(3+b)
(c) 3(3+b)/4(2+b)
(d) 4(3+b)/3(2+b)

Answer: A

Question. A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is
(a) g /L
(b) 2g/L
(c) 2g/3L
(d) 3g/2L

Answer: D

Question. Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D₁ has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s^–1. Disc D₂ has 4kg mass, 0.1 m radius and initial angular velocity of 200 rad s^–1. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad s^–1) of the system is
(a) 40
(b) 60 
(c) 100
(d) 120

Answer: C

Question. When a disc rotates with uniform angular velocity, which of the following is not true?
(a) The sense of rotation remains same
(b) The orientation of the axis of rotation remains same
(c) The speed of rotation is non-zero and remains same
(d) The angular acceleration is non-zero and remains same

Answer: D

Question. A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length.
Which one of the two objects gets to the bottom of the plane first ?
(a) Disk 
(b) Sphere
(c) Both reach at the same time
(d) Depends on their masses

Answer: B

Question. A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s^–2 is :
(a) 25 N
(b) 50 N
(c) 78.5 N
(d) 157 N

Answer: D

Question. Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX' axis is
(a) 3mr²
(b) 16/5 mr²
(c) 4mr²
(d) 11/5 mr²

Answer: C

Question. For which of the following does the centre of mass lie outside the body?
(a) A pencil
(b) A shotput
(c) A dice
(d) A bangle

Answer: D

Question. A force F̅ = αî + 3ĵ + 6k̂is acting at a point r̅ = 2î - 6ĵ - 12k̂ . The value of α for which angular momentum about origin is conserved is : 
(a) 2
(b) zero
(c) 1
(d) –1

Answer: D

Question. A uniform square plate has a small piece Q of an irregular shape removed and glued to the centre of the plate leaving a hole behind in figure. The moment of inertia about the zaxis is then,
(a) increased
(b) decreased
(c) the same
(d) changed in unpredicted manner

Answer: B

Question. The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are
(a) √2 :1
(b) 1: √2
(c) 3 : 2
(d) 2 : 1

Answer: A

Question. A merry-go-round, made of a ring-like platform of radius R and mass M, is revolving with angular speed w. A person of mass M is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round (as seen from the round). The speed of the round of afterwards is
(a) 2ω
(b) ω
(c) ω/2
(d) 0

Answer: A

Question. A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s–2. Its net acceleration in ms–2 at the end of 2.0s is approximately :
(a) 8.0
(b) 7.0 
(c) 6.0
(d) 3.0

Answer: A

Question. The ratio of the accelerations for a solid sphere (mass ‘m’ and radius ‘R’) rolling down an incline of angle ‘q’ without slipping and slipping down the incline without rolling is :
(a) 5 : 7
(b) 2 : 3 
(c) 2 : 5
(d) 7 : 5

Answer: A

Question. An automobile moves on a road with a speed of 54 km h^-1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m². If the vehicle is brought to rest in 15s, the magnitude of average torque transmitted by its brakes to the wheel is : 
(a) 8.58 kg m² s^-2
(b) 10.86 kg m2 s^-2
(c) 2.86 kg m² s^-2
(d) 6.66 kg m² s-2

Answer: D

Question. From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre ?
(a) 15 MR²/32
(b) 13 MR²/32
(c) 11 MR²/32
(d) 9 MR²/32

Answer: B

Question. Which of the following statements are correct ? 
(A) Centre of mass of a body always coincides with the entre of gravity of the body
(B) Centre of mass of a body is the point at which the total gravitational torque on the body is zero
(C) A couple on a body produce both translational and rotation motion in a body
(D) Mechanical advantage greater than one means that small effort can be used to lift a large load
(a) (A) and (B)
(b) (B) and (C)
(c) (C) and (D)
(d) (B) and (D)

Answer: D

Question. Which of the following points is the likely position of the centre of mass of the system shown in figure? (2)
(a) A
(b) B
(c) C
(d) D

Answer: C

Question. Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω₁ and ω₂ . They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:-
(a) 1/4 I(ω₁ - ω₂)²
(b) I(ω₁ - ω₂)²
(c) 1/8 (ω₁ - ω₂)²
(d) 1/2 I(ω₁ - ω₂)²

Answer: A

Question. A mass m moves in a circle on a smooth horizontal plane with velocity v0 at a radius R0. The mass is attached to string which passes through a smooth hole in the plane as shown. 
 
The tension in the string is increased gradually and finally m moves in a circle of radius R0/2. The final value of the kinetic energy is
(a) 1/4 mv₀²
(b) 2mv₀²
(c) 1/2mv₀²
(d) mv0²

Answer: B

1. Two particles in an isolated system under go head on collision. What is the acceleration of the centre of mass of the system?

2. Which component of a force does not contribute towards torque?

3. What is the position of centre of mass of a rectangular lamina?

4. Show that cross product of two parallel vectors is zero?

5. Prove the relation 

that for an isolated system the centre of mass moves with uniform velocity along a straight line path?

7. The angle θ covered by a body in rotational motion is give by the equation θ = 6t +5t² + 2t³. Determine the value of instantaneous angular velocity and angular acceleration at time t = 2S.

8. (a) Which physical quantities are represented by the

(i) Rate of change of angular momentum

(ii) Product of I and  w

(b) Show that angular momentum of a satellite of mass MS revolving around the earth having mass Me in an orbit of radius r is equal to [G Me Ms²r]^1/2

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