CBSE Class 11 Physics System of Particles And Rigid Body Worksheet

UNIT- V SYSTEM OF PARTICLES AND RIGID BODY

SECTION-A CONCEPTUAL & APPLICATION TYPE QUESTIONS

Question. A boy and a man carry a uniform rod of length L, horizontally in such a way that the boy gets 1/4th load. If the boy is at one end of the rod, the distance of the man from the other end is
(a) L/3
(b) L/4
(c) 2 L/3
(d) 3 L/4

Answer: A

Question. Consider a system of two particles having masses m₁ and m₂ . If the particle of mass m₁ is pushed towards the centre of mass particles through a distance d, by what distance would the particle of mass m₂ move so as to keep the mass centre of particles at the original position?
(a) m₂/m₁ d
(b) m₁/m₁+m₂ d
(c) m₁/m₂ d
(d) d

Answer: C

Question. A solid sphere of mass M and radius R is pulled horizontally on a sufficiently rough surface as shown in the figure. 

Choose the correct alternative.
(a) The acceleration of the centre of mass is F/M 
(b) The acceleration of the centre of mass is 2/3 F/M
(c) The friction force on the sphere acts forward
(d) The magnitude of the friction force is F/3

Answer: B,C

Question. If the earth is treated as a sphere of radius R and mass M, its angular momentum about the axis of its diurnal rotation with period T is
(a) 4πMR²/5T
(b) 2πMR²/5T
(c) MR²T/T
(d) πMR³/T

Answer: A

Question. The moment of inertia of a uniform circular disc of radius ‘R’ and mass ‘M’ about an axis passing from the edge of the disc and normal to the disc is
(a) MR²
(b) 1/2 MR²
(c) 3/2 MR²
(d) 7/2 MR²

Answer: C

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 momenta will be in the ratio
(a) 2 : 1
(b) 1 : 2
(c) √2 : 1
(d) 1 : √2

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 tube of length L is filled completely with an incompressible liquid of mass M and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with uniform angular speed ω. What is the force exerted by the liquid at the other end?
(a) MLω²/2
(b) MLω²
(c) MLω²/4
(d) MLω²/8

Answer: A

Question. A circular disk of moment of inertia It is rotating in a horizontal plane, its symmetry axis, with a constant angular speed ωi . Another disk of moment of inertia I_b is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed ω_f . The energy lost by the initially rotating disk to friction is 

Answer: D

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) 3/2 MR²
(b) 2/3 MR²
(c) 5/4 MR²
(d) 4/5 MR²

Answer: C

Question. The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through 
(a) B
(b) C
(c) D
(d) A

Answer: A

Question. A cylinder rolls down an inclined plane of inclination 30°, the acceleration of cylinder is
(a) g/3
(b) g
(c) g/2
(d) 2g/3

Answer: A

Question. The wheel of a car is rotating at the rate of 1200 revolutions per minute. On pressing the accelerator for 10 seconds it starts rotating at 4500 revolutions per minute. The angular acceleration of the wheel is
(a) 30 radian / second²
(b) 1880 degrees/ second²
(c) 40 radian / second²
(d) 1980 degree/second²

Answer: D

Question. A round disc of moment of inertia I₂ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I₁ rotating with an angular velocity w about the same axis. The final angular velocity of the combination of discs is 

Answer: D

Question. A solid sphere of mass 1 kg rolls on a table with linear speed 1 ms–1. Its total kinetic energy is
(a) 1 J
(b) 0.5 J
(c) 0.7 J
(d) 1.4 J

Answer: C

Question. A wheel having moment of inertia 2 kg-m2 about its vertical axis, rotates at the rate of 60 rpm about this axis, The torque which can stop the wheel’s rotation in one minute would be
(a) π/18 Nm
(b) 2π/15 Nm
(c) π/12 Nm
(d) π/15 Nm

Answer: D

Question. Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side/cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm2 units will be
(a) 3/2 ml²
(b) 3/4 ml²
(c) 2 ml²
(d) 5/4 ml²

Answer: D

Question. One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is
(a) 1/2 mR²
(b) 1/4 mR²
(c) 1/8 mR²
(d) √2mR²

Answer: A

Directions for : Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer 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 : If no external force acts on a system of particles, then the centre of mass will not move in any direction.
Statement 2 : If net external force is zero, then the linear momentum of the system remains constant.

Answer: A

Question. Statement 1 : A wheel moving down a frictionless inclined plane will slip and not roll on the plane.
Statement 2 : It is the frictional force which provides a torque necessary for a body to roll on a surface.

Answer: B

Question. Statement 1 : When you lean behind over the hind legs of the chair, the chair falls back after a certain angle.
Statement 2 : Centre of mass lying outside the system makes the system unstable.

Answer: D

Question. Statement 1: A rigid disc rolls without slipping on a fixed rough horizontal surface with uniform angular velocity. Then the acceleration of lowest point on the disc is zero.
Statement 2 : For a rigid disc rolling without slipping on a fixed rough horizontal surface, the velocity of the lowest point on the disc is always zero.

Answer: A
 

1. Does the centre of mass of a solid necessarily lie within body? If not, give an example.

2. Why a force is applied at right angles to the heavy door at outer edge while closing oropening it?

3. Standing is not allowed in double decker bus. Why?

4. A person is sitting in the compartment of a train moving with uniform velocity on smoothmtrack. How will the velocity of C.M. of compartment change if person begins to run in compartment?

5. What is the physical significance of moment of inertia?

6. Is radius of gyration a constant quantity?

7. Why is it more difficult to revolve a stone tied to a large string than a stone tied to a smaller string?

8. While turning the page of book, we usually apply force perpendicular to the plane of the page at farthest end. Explain why?

9. The moments of inertia of two rotating bodies A and B are I_A and IB (I_A>I_B) and their angular momenta are equal. Which one has a greater kinetic energy?

10. State the law of conservation of angular momentum.

11. Explain if the ice on polar caps of earth melts, how will it affect the duration of the day?

12. Torque and work is both equal to force times distance. Then how do they differ?

13. Explain why the speed of whirl wind in a tornado is alarmingly high?

14. State the theorem of perpendicular axes for moment of inertia.

15. State the theorem of parallel axes for moment of inertia.

SECTION-B NUMERICAL QUESTIONS

1. Three identical spheres each of radius R, placed touching each other on a horizontal table. Locate the position of the centre of mass of the system.

2. Three balls of masses 1, 2 and 3 kg respectively are arranged at the corners of an equilateral triangle of side 1m. What will be the M. I. Of the system about an axis through the centroid and perpendicular to the plane of triangle?

3. Calculate the ratio of radii of gyration of circular ring and a disc of same mass and radius about the axis passing through their centres and perpendicular to their planes.

4. A solid cylinder rolls down an inclined plane. Its mass is 2 Kg and radius 0.1. If the height of the inclined plane is 4m, what is its rotational kinetic energy when it reaches the foot of the plane?

5. A flywheel (like disc) of mass 25 kg has radius of 0.2 m. It makes 240 r.p.m. What is the torque necessary to bring it to rest in 20 s? If the torque is due to a force applied tangentially on the rim of the flywheel, what is magnitude of the force?

6. A horizontal disc rotating about a vertical axis passing through its centre makes 180 r.p.m. A small piece of wax of mass 10 g falls vertically on disc and adheres to it at a distance of 8 cm from its axis. If the frequency is thus reduced to 150rpm,calculate the M.I. of disc.

7. A ring, a disc and a sphere all of the same radius and mass roll down an inclined plane from the same height 'h'. Which of the three reaches the bottom (i) earliest (ii) latest?
8. A disc of radius 0.5 m is rotating about an axis passing through its centre and perpendicular to its plane. A tangential force of 2000 N is applied to bring the disc to rest in 2 s. Calculate its angular momentum.

9. A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5g are put one on top of the other at 12.0 cm mark, the stick is found to be balanced at 45.0 cm. What is mass of the metre stick?

10. Find the centre of mass of uniform L-shaped lamina (a thin flat plate) with dimensions as shown in figure. The mass of lamina is 3kg.

11. A solid sphere is rolling on a frictionless surface about its axis of symmetry. Find the rotational energy and the ratio of its rotational energy to its total energy.

12. A ring of diameter 0.4 m and of mass 10 kg is rotating about its axis at the rate of 2100 rpm. Find (i) moment of inertia (ii) angular momentum and (iii) rotational kinetic energy of the ring.

13. A car weighs 1800 kg. The distance between its front and back axles is 1.8 m. Its centre of gravity is 1.05 m behind the front axle. Determine the force exerted by level ground on each front wheel and each back wheel.

14. What will be the duration of the day, if the earth suddenly shrinks to 1/64 of its original volume, mass of earth remains unchanged?

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