Physics Syllabus (JEE Main)

Current Electricity Electrostatics Gravitation Kinematics Kinetic Theory of Gases Laws of Motion Magnetism & EMI Modern Physics Optics Oscillations & Waves Properties of Matter Rotational Motion Thermodynamics Units & Measurement Work, Energy & Power

Q. A rigid body is rotating about a fixed axis with an angular velocity ω. If its moment of inertia is I, what is its angular momentum?

A. Iω
B. ω/I
C. I/ω
D. Iω^2

Solution

Angular momentum L = Iω, where I is the moment of inertia and ω is the angular velocity.

Correct Answer: A — Iω

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Q. A rigid body is rotating about a fixed axis with an angular velocity ω. If the moment of inertia of the body is I, what is its angular momentum?

A. Iω
B. ω/I
C. I/ω
D. Iω^2

Solution

Angular momentum L = Iω, where I is the moment of inertia and ω is the angular velocity.

Correct Answer: A — Iω

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Q. A rigid body is rotating about a fixed axis with an angular velocity ω. If the moment of inertia of the body is I, what is the angular momentum of the body?

A. Iω
B. ω/I
C. I/ω
D. Iω^2

Solution

Angular momentum L = Iω, where I is the moment of inertia and ω is the angular velocity.

Correct Answer: A — Iω

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Q. A rigid body is rotating about a fixed axis. If the moment of inertia of the body is I and it is rotating with an angular velocity ω, what is its angular momentum?

A. Iω
B. I/ω
C. Iω^2
D. ω/I

Solution

Angular momentum L = Iω, where I is the moment of inertia and ω is the angular velocity.

Correct Answer: A — Iω

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Q. A rigid body rotates about a fixed axis with an angular velocity ω. If the moment of inertia of the body is I, what is the angular momentum of the body?

A. Iω
B. ω/I
C. I/ω
D. Iω^2

Solution

Angular momentum L = Iω, where I is the moment of inertia and ω is the angular velocity.

Correct Answer: A — Iω

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Q. A roller coaster at the top of a hill has a height of 30 m. If it has a mass of 500 kg, what is its potential energy? (g = 9.8 m/s²)

A. 14700 J
B. 9800 J
C. 15000 J
D. 5000 J

Solution

Potential energy is given by PE = mgh. Here, PE = 500 * 9.8 * 30 = 14700 J.

Correct Answer: A — 14700 J

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Q. A roller coaster at the top of a hill has a height of 30 m. If it has a mass of 500 kg, what is its potential energy at the top?

A. 1500 J
B. 3000 J
C. 7500 J
D. 15000 J

Solution

Potential energy = mgh = 500 * 9.8 * 30 = 147000 J.

Correct Answer: D — 15000 J

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Q. A roller coaster at the top of a hill has a potential energy of 5000 J. If it descends to a height of 10 m, what is its speed at the bottom? (g = 9.8 m/s²)

A. 10 m/s
B. 20 m/s
C. 30 m/s
D. 40 m/s

Solution

Using conservation of energy, initial PE + KE = final PE + KE. 5000 J = mgh + 0.5mv². Solving gives v = √(2(5000 - mgh)/m) = 30 m/s.

Correct Answer: C — 30 m/s

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Q. A roller coaster starts from rest at a height of 30 m. What is its speed at the lowest point? (g = 9.8 m/s²)

A. 10 m/s
B. 15 m/s
C. 20 m/s
D. 25 m/s

Solution

Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv². Solving gives v = √(2gh) = √(2 * 9.8 * 30) = 24.5 m/s.

Correct Answer: C — 20 m/s

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Q. A roller coaster starts from rest at a height of 50 m. What is its speed at the lowest point?

A. 10 m/s
B. 20 m/s
C. 30 m/s
D. 40 m/s

Solution

Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv^2. Solving gives v = sqrt(2gh) = sqrt(2*9.8*50) = 31.3 m/s.

Correct Answer: C — 30 m/s

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Q. A roller coaster starts from rest at a height of 50 m. What is its speed at the lowest point? (g = 9.8 m/s²)

A. 10 m/s
B. 20 m/s
C. 30 m/s
D. 40 m/s

Solution

Using conservation of energy, mgh = 0.5mv². Thus, v = sqrt(2gh) = sqrt(2 * 9.8 * 50) = 31.3 m/s, approximately 30 m/s.

Correct Answer: C — 30 m/s

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Q. A rolling object has a radius R and rolls with a speed v. What is its total kinetic energy?

A. (1/2)mv^2
B. (1/2)mv^2 + (1/2)Iω^2
C. (1/2)mv^2 + (1/2)mv^2
D. (1/2)mv^2 + (1/2)mv^2/R^2

Solution

The total kinetic energy is the sum of translational and rotational kinetic energy: (1/2)mv^2 + (1/2)Iω^2.

Correct Answer: B — (1/2)mv^2 + (1/2)Iω^2

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Q. A rolling object has a total kinetic energy of K. If it is a solid sphere, what is the translational kinetic energy?

A. K/5
B. K/3
C. K/2
D. K/7

Solution

For a solid sphere, the translational kinetic energy is K/3 of the total kinetic energy.

Correct Answer: B — K/3

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Q. A rolling object has both translational and rotational motion. Which of the following quantities remains constant for a rolling object on a flat surface?

A. Linear velocity
B. Angular velocity
C. Total energy
D. Kinetic energy

Solution

The total energy remains constant for a rolling object on a flat surface, assuming no external work is done.

Correct Answer: C — Total energy

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Q. A rotating body has an angular momentum L. If its moment of inertia is I, what is the angular velocity ω of the body?

A. L/I
B. I/L
C. L^2/I
D. IL

Solution

Angular momentum L is given by L = Iω, thus ω = L/I.

Correct Answer: A — L/I

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Q. A rotating disc has a radius R and is spinning with an angular velocity ω. What is the linear speed of a point on the edge of the disc?

A. Rω
B. ω/R
C. R/ω
D. ω

Solution

The linear speed v of a point on the edge of the disc is given by v = Rω.

Correct Answer: A — Rω

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Q. A rotating disc has an angular velocity of ω. If the radius of the disc is doubled while keeping the mass constant, what happens to the angular momentum?

A. It doubles
B. It remains the same
C. It quadruples
D. It halves

Solution

Angular momentum L = Iω, where I is the moment of inertia. If radius is doubled, I increases by a factor of 4, but ω decreases by a factor of 2, so L remains the same.

Correct Answer: A — It doubles

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Q. A rotating object has a kinetic energy of 100 J. If its angular velocity is doubled, what will be its new kinetic energy?

A. 100 J
B. 200 J
C. 400 J
D. 800 J

Solution

Kinetic energy of rotation is given by KE = (1/2)Iω². If ω is doubled, KE becomes (1/2)I(2ω)² = 4(1/2)Iω² = 4KE = 400 J.

Correct Answer: C — 400 J

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Q. A rotating object has a moment of inertia of 3 kg·m² and is rotating with an angular velocity of 10 rad/s. What is its rotational kinetic energy?

A. 15 J
B. 30 J
C. 50 J
D. 100 J

Solution

Rotational kinetic energy K = (1/2)Iω² = (1/2)(3 kg·m²)(10 rad/s)² = 150 J.

Correct Answer: B — 30 J

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Q. A rotating object has an angular momentum L. If the moment of inertia of the object is doubled while keeping the angular velocity constant, what happens to the angular momentum?

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

Angular momentum L = Iω. If I is doubled and ω remains constant, L also doubles.

Correct Answer: A — It doubles

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Q. A rotating object has an angular momentum of 10 kg·m²/s and a moment of inertia of 2 kg·m². What is its angular velocity?

A. 5 rad/s
B. 2 rad/s
C. 10 rad/s
D. 20 rad/s

Solution

Using L = Iω, we find ω = L/I = 10/2 = 5 rad/s.

Correct Answer: A — 5 rad/s

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Q. A rotating object has an angular momentum of 10 kg·m²/s. If its moment of inertia is 2 kg·m², what is its angular velocity?

A. 5 rad/s
B. 2 rad/s
C. 10 rad/s
D. 20 rad/s

Solution

Using L = Iω, we have ω = L/I = 10 kg·m²/s / 2 kg·m² = 5 rad/s.

Correct Answer: A — 5 rad/s

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Q. A rotating object has an angular momentum of 12 kg·m²/s and a moment of inertia of 4 kg·m². What is its angular velocity?

A. 3 rad/s
B. 4 rad/s
C. 2 rad/s
D. 1 rad/s

Solution

Angular momentum L = Iω, thus ω = L/I = 12 kg·m²/s / 4 kg·m² = 3 rad/s.

Correct Answer: A — 3 rad/s

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Q. A rotating object has an angular momentum of 15 kg·m²/s. If its moment of inertia is 3 kg·m², what is its angular velocity?

A. 5 rad/s
B. 10 rad/s
C. 15 rad/s
D. 20 rad/s

Solution

Angular momentum L = Iω, thus ω = L/I = 15 kg·m²/s / 3 kg·m² = 5 rad/s.

Correct Answer: B — 10 rad/s

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Q. A rotating object has an angular momentum of L. If its angular velocity is doubled and its moment of inertia remains constant, what will be the new angular momentum?

A. L
B. 2L
C. 4L
D. L/2

Solution

Angular momentum L = Iω, if ω is doubled, L becomes 2I(2ω) = 4L.

Correct Answer: C — 4L

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Q. A rotating object has an angular momentum of L. If its moment of inertia is doubled while keeping the angular velocity constant, what will happen to its angular momentum?

A. It doubles
B. It halves
C. It remains the same
D. It becomes zero

Solution

Angular momentum L = Iω; if I is doubled and ω remains constant, L remains the same.

Correct Answer: C — It remains the same

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Q. A rotating object has an angular momentum of L. If its moment of inertia is halved and its angular velocity is doubled, what is the new angular momentum?

A. L
B. 2L
C. 4L
D. L/2

Solution

New angular momentum L' = I'ω' = (1/2I)(2ω) = L.

Correct Answer: C — 4L

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Q. A rotating object has an angular momentum of L. If its moment of inertia is halved and the angular velocity is doubled, what is the new angular momentum?

A. L
B. 2L
C. 4L
D. L/2

Solution

New angular momentum L' = I'ω' = (1/2 I)(2ω) = Iω = L.

Correct Answer: C — 4L

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Q. A rotating object has an angular velocity of 30 rad/s and a moment of inertia of 3 kg·m². What is its rotational kinetic energy?

A. 135 J
B. 450 J
C. 270 J
D. 90 J

Solution

Rotational kinetic energy K = (1/2)Iω² = (1/2)(3 kg·m²)(30 rad/s)² = 450 J.

Correct Answer: B — 450 J

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Q. A rotating object has an angular velocity of 30 rad/s. If it is brought to rest in 5 seconds, what is the angular deceleration?

A. 6 rad/s²
B. 5 rad/s²
C. 3 rad/s²
D. 4 rad/s²

Solution

Angular deceleration = (final angular velocity - initial angular velocity) / time = (0 - 30 rad/s) / 5 s = -6 rad/s².

Correct Answer: A — 6 rad/s²

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Physics Syllabus (JEE Main)

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