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

10 NEET-UG practice questions on System of Particles & Rotational Motion, part of Physics. The first 10 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
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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
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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
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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
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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
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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

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?