CBSE Class 11 Physics System of Particles and Rotational Motion Worksheet Set A

Question. Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass. The centre of mass of the system from the 5 kg particle is nearly at a distance of
(a) 33 cm
(b) 50 cm
(c) 67 cm
(d) 80 cm 
Answer. C

Question. Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm.
The distance of the centre of mass from the origin is
(a) 40 cm
(b) 45 cm
(c) 50 cm
(d) 30 cm
Answer. A

Question. Three identical metal balls, each of radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed when centres of three balls are joined. The centre of the mass of the system is located at
(a) line joining centres of any two balls
(b) centre of one of the balls
(c) horizontal surface
(d) point of intersection of the medians. 
Answer. D

Question.The centre of mass of system of particles does not depend on
(a) position of the particles
(b) relative distances between the particles
(c) masses of the particles
(d) forces acting on the particle.
Answer. D 

Question. Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the center of mass of the system shifts by
(a) 3.0 m
(b) 2.3 m
(c) zero
(d) 0.75 m
Answer. C

Question. Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be
(a) 2v
(b) zero
(c) 1.5v
(d) v 
Answer. B

Question. A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s.When the stone reaches the floor, the distance of the man above the floor will be
(a) 9.9 m
(b) 10.1 m
(c) 10 m
(d) 20 m
Answer. B

Question. When a mass is rotating in a plane about a fixed point, its angular momentum is directed along
(a) a line perpendicular to the plane of rotation
(b) the line making an angle of 45° to the plane of rotation
(c) the radius
(d) the tangent to the orbit.
Answer. A

Question. A particle of mass m = 5 is moving with a uniform speed v =3 √2 in the XOY plane along the line y = x + 4. The magnitude of the angular momentum of the particle about the origin is
(a) 60 units
(b) 40 √2 units
(c) zero
(d) 7.5 units 
Answer. A

Question. Which of the following statements are correct?
(1) Centre of mass of a body always coincides with the centre of gravity of the body.
(2) Centre of mass of a body is the point at which the total gravitational torque on the body is zero.
(3) A couple on a body produces both translational and rotational motion in a body.
(4) Mechanical advantage greater than one means that small effort can be used to lift a large load.
(a) (1) and (2)
(b) (2) and (3)
(c) (3) and (4)
(d) (2) and (4)
Answer. *

Question. (1) Centre of gravity (C.G.) of a body is the point at which the weight of the body acts.
(2) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius.
(3) To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its C.G.
(4) The radius of gyration of any body rotating about an axis is the length of the perpendicular drawn from the C.G. of the body to the axis.
Which one of the following pairs of statements is correct?
(a) (4) and (1)
(b) (1) and (2)
(c) (2) and (3)
(d) (3) and (4)
Answer. A

Question. A rod of length 3 m and its mass per unit length is directly proportional to distance x from one of its end then its centre of gravity from that end will be at
(a) 1.5 m
(b) 2 m
(c) 2.5 m
(d) 3.0 m 
Answer. B

Question. 250 N force is required to raise 75 kg mass from a pulley. If rope is pulled 12 m then the load is lifted to 3 m, the efficiency of pulley system will be
(a) 25%
(b) 33.3%
(c) 75%
(d) 90%.
Answer. C

Question. A couple produces
(a) linear and rotational motion
(b) no motion
(c) purely linear motion
(d) purely rotational motion.
Answer. D

Question. A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere.
The ratio of their kinetic energies of rotation (E_sphere/E_cylinder) will be
(a) 2 : 3
(b) 1 : 5
(c) 1 : 4
(d) 3 : 1
Answer. B

Question. The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is
(a) √2 :1
(b) √2 : √3
(c) √3 : √2
(d) 1: √2 
Answer. D

Question. Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be in the ratio
(a) 2 : 1
(b) 1 : 2
(c) √2 : 1
(d) 1 : √2
Answer. C 

Question. A circular disc is to be made by using iron and aluminium so that it acquires maximum moment of inertia about geometrical axis. It is possible with
(a) aluminium at interior and iron surrounding it
(b) iron at interior and aluminium surrounding it
(c) using iron and aluminium layers in alternate order
(d) sheet of iron is used at both external surface and aluminium sheet as internal layers.
Answer. A

Question. A fly wheel rotating about fixed axis has a kinetic energy of 360 joule when its angular speed is 30 radian/sec. The moment of inertia of the wheel about the axis of rotation is
(a) 0.6 kg m²
(b) 0.15 kg m²
(c) 0.8 kg m²
(d) 0.75 kg m²
Answer. C

Question. A ring of mass m and radius r rotates about an axis passing through its centre and perpendicular to its plane with angular velocity w. Its kinetic energy is
(a) 1/2 mr²ω²
(b) mrw²
(c) mr²w²
(d) 1/2 mrω²
Answer. A

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) 11 MR²/32
(b) 9 MR²/32
(c) 15 MR²/32
(d) 13 MR²/32 
Answer. D

Question. The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is
(a) I₀ + ML²/2
(b) I₀ + ML²/4
(c) I₀ + 2ML²
(d) I₀ + ML
Answer. B

Question. Four identical thin rods each of mass M and length l, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is
(a) 2/3Ml²
(b) 13/3 Ml²
(c) 1/3 Ml²
(d) 4/3 Ml²
Answer. D

Question. A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90°. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is
(a) ML² /6
(b) √2 ML²/24
(c) ML²/24
(d) ML²/12
Answer. D

Question. The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc
(a) 1/2 MR²
(b) MR²
(c) 2/5 MR2R²
(d) 3/2 MR²
Answer. D

Question. The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius and mass about a tangential axis in the plane of the ring is
(a) 2 : 3
(b) 2 : 1
(c) √5 : √6
(d) 1: √2
Answer. C

Question. The moment of inertia of a disc of mass M and radius R about an axis, which is tangential to the circumference of the disc and parallel to its diameter is
(a) 5/4 MR²
(b) 2/3 MR²
(c) 3/2 MR²
(d) 4/5 MR²
Answer. A

Question. Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be
(a) 5I
(b) 3I
(c) 6I
(d) 4I
Answer. C

Question. A wheel has angular acceleration of 3.0 rad/sec² and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radians) of
(a) 10
(b) 12
(c) 4
(d) 6
Answer. A

Question. A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop it after 2p revolutions is
(a) 2 × 10⁶ N m
(b) 2 × 10^–6 N m
(c) 2 × 10^–3 N m
(d) 12 × 10^–4 N m
Answer. B

Question. Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed w about their own symmetry axes.The amounts of work (W) required to bring them to rest, would satisfy the relation
(a) W_C > W_B > W_A
(b) W_A > W_B > W_C
(c) W_B > W_A > W_C
(d) W_A > W_C > W_B
Answer. A

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 s^–2
(b) 25 rad s^–2
(c) 5 m s^–2
(d) 25 ms^–2
Answer. B

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 m s^–2 at the end of 2.0 s is approximately
(a) 6.0
(b) 3.0
(c) 8.0
(d) 7.0
Answer. C

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 15 s, the magnitude of average torque transmitted by its brakes to the wheel is
(a) 10.86 kg m² s^–2
(b) 2.86 kg m²s^–2
(c) 6.66 kg m² s^–2
(d) 8.58 kg m² s^–2
Answer. C

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. The instantaneous angular position of a point on a rotating wheel is given by the equation q(t) = 2t³ – 6t².The torque on the wheel becomes zero at
(a) t = 1 s
(b) t = 0.5 s
(c) t = 0.25 s
(d) t = 2 s
Answer. A

Question. The moment of inertia of a body about a given axis is 1.2 kg m². Initially, the body is at rest. In order to produce a rotational kinetic energy of 1500 joule, an angular acceleration of 25 radian/sec² must be applied about that axis for a duration of
(a) 4 s
(b) 2 s
(c) 8 s
(d) 10 s
Answer. B

Question. A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?
(a) Angular velocity.
(b) Moment of inertia.
(c) Rotational kinetic energy.
(d) Angular momentum.
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 4 kg 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) 60
(b) 100
(c) 120
(d) 40
Answer. B

Question. A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg m². It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 m s^–1 relative to the ground. Time taken by the man to complete one revolution is
(a) π s
(b) 3π/2 s
(c) 2π s
(d) π/2 s
Answer. C

Question. A disc is rotating with angular speed w. If a child sits on it, what is conserved?
(a) linear momentum.
(b) angular momentum.
(c) kinetic energy.
(d) potential energy.
Answer. B

Question. A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it ?
(a) 1 J
(b) 3 J
(c) 30 kJ
(d) 2 J
Answer. B

Question. A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle inclination 30°.The centre of mass of cylinder has speed of 4 m/s.The distance travelled by the cylinder on the incline surface will be (Take g = 10 m/s²)
(a) 2.2 m
(b) 1.6 m
(c) 1.2 m
(d) 2.4 m
Answer. D

Question. A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously.The ratio Kt : (Kt + Kr) for the sphere is
(a) 7 : 10
(b) 5 : 7
(c) 10 : 7
(d) 2 : 5
Answer. B

Question. A disc 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) Both reach at the same time
(b) Depends on their masses
(c) Disc
(d) Sphere
Answer. D

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. A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m s^–1. It collides with a horizontal spring of force constant 200 N m^–1. The maximum compression produced in the spring will be
(a) 0.5 m
(b) 0.6 m
(c) 0.7 m
(d) 0.2 m
Answer. B

Question. A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?
(a) Both together only when angle of inclination of plane is 45°.
(b) Both together.
(c) Hollow cylinder.
(d) Solid cylinder. 
Answer. D

Question. A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle q. The frictional force
(a) dissipates energy as heat
(b) decreases the rotational motion
(c) decreases the rotational and translational motion
(d) converts translational energy to rotational energy.
Answer. D

Question. A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct?
 (a) h = R
(b) h = 2R
(c) h = 0
(d) no relation between h and R. 
Answer. D

Question. A disc is rolling, the velocity of its centre of mass is vcm. Which one will be correct?
(a) The velocity of highest point is 2 vcm and at point of contact is zero.
(b) The velocity of highest point is vcm and at point of contact is vcm.
(c) The velocity of highest point is 2vcm and point of contact is vcm.
(d) The velocity of highest point is 2vcm and point of contact is 2vcm.
Answer. A

Question. A solid spherical ball rolls on a table. Ratio of its rotational kinetic energy to total kinetic energy is
(a) 1/2
(b) 1/6
(c) 7/10
(d) 2/7
Answer. D

Question. A solid sphere, disc and solid cylinder all of the same mass and radius are allowed to roll down (from rest) on the inclined plane, then
(a) solid sphere reaches the bottom first
(b) solid sphere reaches the bottom last
(c) disc will reach the bottom first
(d) all reach the bottom at the same time. 
Answer. A

Question. A solid homogenous sphere of mass M and radius is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere
(a) total kinetic energy is conserved
(b) the angular momentum of the sphere about the point of contact with the plane is conserved
(c) only the rotational kinetic energy about the centre of mass is conserved
(d) angular momentum about the centre of mass is conserved.
Answer. B