No net external force acts on a system of particles. What can be said about its centre of mass?

It stays at rest or moves with constant velocity

It moves with constant acceleration

Assertion A: An ice skater spinning with outstretched arms speeds up when the arms are pulled in. Reason R: Pulling the arms in produces a net external torque on the skater about the spin axis. Choose the correct answer.

A is correct but R is not correct

A is not correct but R is correct

Both A and R are correct and R is the correct explanation of A

Both A and R are correct but R is not the correct explanation of A

System of Particles & Rotational Motion

29 NEET-UG practice questions on System of Particles & Rotational Motion, part of Physics. The first 25 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

Question 1 · Easy
No net external force acts on a system of particles. What can be said about its centre of mass?
1. AIt moves with constant acceleration
2. BIt always moves in a circle
3. CIt stays at rest or moves with constant velocity
4. DIt always stays at rest
Show answerHide answer
Answer: C · It stays at rest or moves with constant velocity
M × (acceleration of the centre of mass) equals the net external force. With no external force, this acceleration is zero, so the centre-of-mass velocity stays constant. Internal forces cannot change it.
- A: This would need a non-zero external force.
- B: Circular motion also requires a net external force.
- D: This ignores that it can keep moving uniformly.
Remember this
Only external forces change the motion of the centre of mass.
Question 2 · Easy
Arrange these bodies, each of the same mass and radius, in increasing order of moment of inertia about an axis through the centre (perpendicular to the plane for the flat ones, a diameter for the spheres). A. Thin ring B. Uniform disc C. Solid sphere D. Thin hollow sphere
1. AA, D, B, C
2. BC, B, D, A
3. CC, D, B, A
4. DB, C, D, A
Show answerHide answer
Answer: B · C, B, D, A
The moments of inertia are: solid sphere (2/5)MR², disc (1/2)MR², hollow sphere (2/3)MR² and ring MR². Mass placed farther from the axis gives a larger value.
- A: This reverses the order, ranking from largest to smallest.
- C: This puts the hollow sphere (2/3) below the disc (1/2).
- D: This puts the disc (1/2) below the solid sphere (2/5).
Remember this
The ring, with all its mass at distance R, has the largest value; the solid sphere has the least.
Question 3 · Medium
A uniform disc is released from rest on an incline and rolls down without slipping through a vertical height of 2.7 m. Taking g = 10 m/s², what is the speed of its centre at the bottom?
1. A5.2 m/s
2. B6.0 m/s
3. C6.2 m/s
4. D7.3 m/s
Show answerHide answer
Answer: B · 6.0 m/s
Energy: mgh = (1/2)mv² + (1/2)(mR²/2)(v/R)² = (3/4)mv². So v² = (4/3)(10)(2.7) = 36 and v = 6 m/s. Check with v² = 2gh/(1 + k²/R²) = 54/1.5 = 36.
- A: This uses k²/R² = 1, the value for a ring.
- C: This uses k²/R² = 2/5, the value for a solid sphere.
- D: This ignores rotational energy, as for frictionless sliding.
Remember this
In rolling, v² = 2gh/(1 + k²/R²); a smaller k²/R² means a higher speed at the bottom.
Question 4 · Medium
Assertion A: An ice skater spinning with outstretched arms speeds up when the arms are pulled in. Reason R: Pulling the arms in produces a net external torque on the skater about the spin axis. Choose the correct answer.
1. AA is not correct but R is correct
2. BA is correct but R is not correct
3. CBoth A and R are correct and R is the correct explanation of A
4. DBoth A and R are correct but R is not the correct explanation of A
Show answerHide answer
Answer: B · A is correct but R is not correct
Pulling in the arms lowers the moment of inertia. With almost no external torque about the axis, Iω stays constant, so ω rises, and A is true. The pull is an internal force and gives no external torque, so R is false.
- A: A is correct: the skater does spin faster.
- C: R is false, so it cannot explain A.
- D: R is false, since the forces in the arms are internal.
Remember this
Angular momentum is conserved when external torque is zero; internal forces can change I, and hence ω.
Question 5 · Hard
A light string wound on a uniform solid cylinder (mass 4 kg, radius 0.1 m), free to turn about its fixed horizontal axis, carries a 2 kg block at its free end. Taking g = 10 m/s², what is the angular acceleration of the cylinder when the block is released?
1. A100 rad/s²
2. B50 rad/s²
3. C33.3 rad/s²
4. D66.7 rad/s²
Show answerHide answer
Answer: B · 50 rad/s²
For the block, 20 − T = 2a. For the cylinder, TR = (1/2)MR²(a/R), so T = (M/2)a = 2a. Then 20 = 4a, a = 5 m/s², and α = a/R = 5/0.1 = 50 rad/s². Check: T = 10 N, and α = TR/I = 1/0.02 = 50.
- A: This takes T = mg, as if the block fell freely.
- C: This uses I = MR², the value for a ring.
- D: This uses I = MR²/4, the value for a disc about a diameter.
Remember this
A hanging mass on a wound cylinder has a = mg/(m + M/2), always less than g.
Question 6 · Medium
A uniform thin disc has a mass of 2 kg and a radius of 0.2 m. Find its moment of inertia about a tangent lying in its own plane.
1. A0.04 kg m²
2. B0.12 kg m²
3. C0.02 kg m²
4. D0.10 kg m²
Answer and explanation in LearnFree account
Question 7 · Medium
Four equal point masses sit at the corners of a light square frame. Find the moment of inertia about the dashed axis drawn in the plane of the frame.
Figure: MedExams
1. A4 kg m²
2. B8 kg m²
3. C2 kg m²
4. D1 kg m²
Answer and explanation in LearnFree account
Question 8 · Medium
Assertion A: The disc shown, initially at rest and free on a smooth horizontal table, gains angular acceleration while its centre of mass stays at rest. Reason R: The torque of a couple has different values about different points. Choose the correct answer.
Figure: MedExams
1. AA is correct but R is not correct
2. BBoth A and R are correct but R is not the correct explanation of A
3. CA is not correct but R is correct
4. DBoth A and R are correct and R is the correct explanation of A
Answer and explanation in LearnFree account
Question 9 · Easy
Three point masses lie in a plane at the grid positions marked. Where is their centre of mass?
Figure: MedExams
1. A(1.5 m, 2 m)
2. B(2 m, 1.5 m)
3. C(2 m, 1 m)
4. D(2 m, 3 m)
Answer and explanation in LearnFree account
Question 10 · Hard
With the speed shown at the foot of the incline, a solid cylinder rolls up without slipping. Taking g = 10 m/s², how far along the incline does it travel before stopping?
Figure: MedExams
1. A3.6 m
2. B7.2 m
3. C5.4 m
4. D2.7 m
Answer and explanation in LearnFree account
Question 11 · Medium
Calculate the torque about the origin of a force F = (3î + ĵ) N acting at the point with position vector r = (î + 2ĵ) m.
1. A7k̂ N m
2. B5k̂ N m
3. C−7k̂ N m
4. D−5k̂ N m
Answer and explanation in LearnFree account
Question 12 · Medium
Match List-I with List-II. List-I (Object rolling on a level floor without slipping) A. Thin hoop B. Uniform circular plate C. Solid ball D. Thin spherical shell List-II (Share of its kinetic energy that is rotational) I. 2/5 II. 1/2 III. 2/7 IV. 1/3 Choose the correct answer from the options given below.
1. AA-II, B-IV, C-I, D-III
2. BA-II, B-III, C-IV, D-I
3. CA-II, B-IV, C-III, D-I
4. DA-IV, B-II, C-III, D-I
Answer and explanation in LearnFree account
Question 13 · Easy
The moment of inertia of a rigid body about a given axis does NOT depend on
1. AThe position of the axis of rotation
2. BIts mass
3. CIts angular velocity
4. DThe way its mass is distributed
Answer and explanation in LearnFree account
Question 14 · Medium
A disc spins freely about a vertical axis through its centre. An identical disc, not rotating, is gently dropped on it so that both share the same axis and soon turn together. What fraction of the original kinetic energy is lost?
1. A25%
2. BZero
3. C50%
4. D75%
Answer and explanation in LearnFree account
Question 15 · Hard
A uniform rod of length 1.2 m is pivoted freely at one end and held horizontal. It is released from rest. Taking g = 10 m/s², what is the speed of its free end when the rod passes through the vertical position?
1. A4.9 m/s
2. B3.5 m/s
3. C3.0 m/s
4. D6 m/s
Answer and explanation in LearnFree account
Question 16 · Easy
In rotational motion, which quantity plays the role that mass plays in linear motion?
1. AAngular momentum
2. BMoment of inertia
3. CTorque
4. DAngular velocity
Answer and explanation in LearnFree account
Question 17 · Medium
A light string is wound on a wheel of radius 0.2 m and moment of inertia 0.5 kg m², free to turn about a fixed horizontal axle. The string is pulled with a steady force of 10 N. Starting from rest, through what angle does the wheel turn in 5 s?
1. A20 rad
2. B100 rad
3. C50 rad
4. D25 rad
Answer and explanation in LearnFree account
Question 18 · Medium
A man stands on a frictionless turntable holding weights at arm's length; the system has a moment of inertia of 6 kg m² and turns at 2 rev/s. He pulls the weights in, reducing the moment of inertia to 2 kg m². What is the ratio of the final rotational kinetic energy to the initial one?
1. A9
2. B3
3. C1/3
4. D1
Answer and explanation in LearnFree account
Question 19 · Medium
A wheel rolls without slipping on a horizontal road, its centre moving at speed v. A. The point of the wheel touching the road is momentarily at rest. B. The topmost point of the wheel moves at speed 2v. C. The kinetic energy of the wheel is purely translational. D. Every point on the rim moves at the same speed v relative to the road. Which of the statements given above are correct?
1. AA and B only
2. BA and D only
3. CA, B and C only
4. DB and D only
Answer and explanation in LearnFree account
Question 20 · Hard
A solid sphere and a ring, each of radius R, are released together from rest at the top of the same rough incline and roll down without slipping. What is the ratio of the time taken by the sphere to the time taken by the ring to reach the bottom?
1. A√(10/7)
2. B1
3. C√(7/10)
4. D7/10
Answer and explanation in LearnFree account
Question 21 · Medium
A uniform disc of mass 2 kg and radius 0.5 m rotates freely at 12 rad/s about its axis. A small 1 kg piece of putty is placed gently on its rim and sticks. What is the new angular speed?
1. A6 rad/s
2. B24 rad/s
3. C8 rad/s
4. D12 rad/s
Answer and explanation in LearnFree account
Question 22 · Hard
A ring and a disc have the same mass and the same radius. Starting from rest, each is turned about its own central axis (perpendicular to its plane) by equal constant torques for the same time. What is the ratio of the kinetic energy of the ring to that of the disc?
1. A1/2
2. B2
3. C1/4
4. D1
Answer and explanation in LearnFree account
Question 23 · Medium
Match List-I (linear motion) with List-II (its rotational analogue). List-I A. Mass B. Force C. Linear momentum D. Kinetic energy (1/2)mv² List-II I. Torque II. (1/2)Iω² III. Moment of inertia IV. Angular momentum Choose the correct answer from the options given below.
1. AA-III, B-I, C-II, D-IV
2. BA-III, B-IV, C-I, D-II
3. CA-III, B-I, C-IV, D-II
4. DA-I, B-III, C-IV, D-II
Answer and explanation in LearnFree account
Question 24 · Hard
A uniform rod of length 1 m is hinged at one end and held horizontal. Taking g = 10 m/s², what is the linear acceleration of its free end just after it is released?
1. A60 m/s²
2. B10 m/s²
3. C7.5 m/s²
4. D15 m/s²
Answer and explanation in LearnFree account
Question 25 · Medium
The speed of a flywheel rises uniformly from 600 rpm to 1200 rpm in 10 s. What is its angular acceleration?
1. Aπ rad/s²
2. B4π rad/s²
3. C2π rad/s²
4. D60 rad/s²
Answer and explanation in LearnFree account

4 more System of Particles & Rotational Motion questions

Answer them one by one, keep your score and see your weak topics in Learn. Signed-out visitors try 25 per exam; sign in with Google to see them all.

Study Physics

System of Particles & Rotational Motion

No net external force acts on a system of particles. What can be said about its centre of mass?

Arrange these bodies, each of the same mass and radius, in increasing order of moment of inertia about an axis through the centre (perpendicular to the plane for the flat ones, a diameter for the spheres). A. Thin ring B. Uniform disc C. Solid sphere D. Thin hollow sphere

A uniform disc is released from rest on an incline and rolls down without slipping through a vertical height of 2.7 m. Taking g = 10 m/s², what is the speed of its centre at the bottom?

Assertion A: An ice skater spinning with outstretched arms speeds up when the arms are pulled in. Reason R: Pulling the arms in produces a net external torque on the skater about the spin axis. Choose the correct answer.

A light string wound on a uniform solid cylinder (mass 4 kg, radius 0.1 m), free to turn about its fixed horizontal axis, carries a 2 kg block at its free end. Taking g = 10 m/s², what is the angular acceleration of the cylinder when the block is released?

A uniform thin disc has a mass of 2 kg and a radius of 0.2 m. Find its moment of inertia about a tangent lying in its own plane.

Four equal point masses sit at the corners of a light square frame. Find the moment of inertia about the dashed axis drawn in the plane of the frame.

Assertion A: The disc shown, initially at rest and free on a smooth horizontal table, gains angular acceleration while its centre of mass stays at rest. Reason R: The torque of a couple has different values about different points. Choose the correct answer.

Three point masses lie in a plane at the grid positions marked. Where is their centre of mass?

With the speed shown at the foot of the incline, a solid cylinder rolls up without slipping. Taking g = 10 m/s², how far along the incline does it travel before stopping?

Calculate the torque about the origin of a force F = (3î + ĵ) N acting at the point with position vector r = (î + 2ĵ) m.

The moment of inertia of a rigid body about a given axis does NOT depend on

A disc spins freely about a vertical axis through its centre. An identical disc, not rotating, is gently dropped on it so that both share the same axis and soon turn together. What fraction of the original kinetic energy is lost?

A uniform rod of length 1.2 m is pivoted freely at one end and held horizontal. It is released from rest. Taking g = 10 m/s², what is the speed of its free end when the rod passes through the vertical position?

In rotational motion, which quantity plays the role that mass plays in linear motion?

A light string is wound on a wheel of radius 0.2 m and moment of inertia 0.5 kg m², free to turn about a fixed horizontal axle. The string is pulled with a steady force of 10 N. Starting from rest, through what angle does the wheel turn in 5 s?

A man stands on a frictionless turntable holding weights at arm's length; the system has a moment of inertia of 6 kg m² and turns at 2 rev/s. He pulls the weights in, reducing the moment of inertia to 2 kg m². What is the ratio of the final rotational kinetic energy to the initial one?

A solid sphere and a ring, each of radius R, are released together from rest at the top of the same rough incline and roll down without slipping. What is the ratio of the time taken by the sphere to the time taken by the ring to reach the bottom?

A uniform disc of mass 2 kg and radius 0.5 m rotates freely at 12 rad/s about its axis. A small 1 kg piece of putty is placed gently on its rim and sticks. What is the new angular speed?

A ring and a disc have the same mass and the same radius. Starting from rest, each is turned about its own central axis (perpendicular to its plane) by equal constant torques for the same time. What is the ratio of the kinetic energy of the ring to that of the disc?

Match List-I (linear motion) with List-II (its rotational analogue). List-I A. Mass B. Force C. Linear momentum D. Kinetic energy (1/2)mv² List-II I. Torque II. (1/2)Iω² III. Moment of inertia IV. Angular momentum Choose the correct answer from the options given below.

A uniform rod of length 1 m is hinged at one end and held horizontal. Taking g = 10 m/s², what is the linear acceleration of its free end just after it is released?

The speed of a flywheel rises uniformly from 600 rpm to 1200 rpm in 10 s. What is its angular acceleration?