Equilibrium of rigid bodies and equations of rotational motion — NEET & JEE Questions

Question 1 · difficulty L1 · recall

For a rigid body to be in complete static equilibrium, the net force and net torque must both be

• A. zero
• B. maximum
• C. parallel
• D. equal to its weight

Question 2 · difficulty L2 · understanding

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle $\theta_1$ and in the next 2 s it rotates through an angle $\theta_2$. The ratio $\frac{\theta_2}{\theta_1}$ is $\_\_\_\_$ .

• A. 6
• B. 3
• C. 4
• D. ${\frac{1}{3}}$

Question 3 · difficulty L2 · understanding

The rotational analogue of Newton's second law for a rigid body about a fixed axis is

• A. $\tau=I\alpha$
• B. $F=ma$
• C. $L=I/\omega$
• D. $\tau=I/\alpha$

Question 4 · difficulty L2 · understanding

A nonzero net torque on a rigid body primarily produces

• A. angular acceleration
• B. constant angular velocity necessarily
• C. zero rotation
• D. linear momentum conservation only

Question 5 · difficulty L3 · understanding

A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm . It is brought to rest in 10 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are $\_\_\_\_$ and $\_\_\_\_$ respectively.

• A. $0.128 \pi \mathrm{Nm}, 100$
• B. $0.0128 \pi \mathrm{Nm}, 50$
• C. $0.128 \pi \mathrm{Nm}, 50$
• D. $0.0128 \pi \mathrm{Nm}, 100$

Question 6 · difficulty L3 · understanding

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m , would be:

• A. 20 rad/s
• B. 30 rad/s
• C. 10 rad/s
• D. 0 rad/s

Question 7 · difficulty L3 · understanding

A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is ________ J. ($g = 10~\mathrm{m/s^2}$)

Question 8 · difficulty L3 · application

A wheel has moment of inertia $2\,\text{kg m}^2$ and experiences net torque 6 N m. What is its angular acceleration?

• A. 3 rad s$^{-2}$
• B. 12 rad s$^{-2}$
• C. 0.33 rad s$^{-2}$
• D. 8 rad s$^{-2}$

Question 9 · difficulty L4 · application

A uniform horizontal beam is supported at its centre. Equal downward forces act at equal distances on opposite sides. What is the net torque about the centre?

• A. Zero
• B. Clockwise and nonzero
• C. Anticlockwise and nonzero
• D. Equal to the sum of force magnitudes

Question 10 · difficulty L4 · application

A 20 N force acts perpendicular to a lever arm 0.50 m from a pivot. What torque magnitude is produced?

• A. 10 N m
• B. 40 N m
• C. 20 N m
• D. 0.025 N m