Four \(2~\text{kg}\) masses are connected by \(\dfrac{1}{4}~\text{m}\) spokes to an axle as in figure given below. A force \(F\) of \(24~\text{N}\) acts on a lever \(\dfrac{1}{2}~\text{m}\) long to produce an angular acceleration \(\mathit{\alpha}\). The magnitude of \(\mathit{\alpha}\) (in rad/s2) is:
     
1. \(2\) 2. \(12\)
3. \(6\) 4. \(3\)

Subtopic:  Torque |
 76%
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Given below are two statements: 
Assertion (A): The centre-of-mass of an isolated system of particles remains at rest if it is initially at rest.
Reason (R): Internal forces acting within a system cannot change the velocity of the centre-of-mass which is proportional to the total momentum of the system.
 
1. (A) is True but (R) is False.
2. (A) is False but (R) is True.
3. Both (A) and (R) are True and (R) is the correct explanation of (A).
4. Both (A) and (R) are True but (R) is not the correct explanation of (A).
Subtopic:  Center of Mass |
 76%
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A wheel is subjected to uniform angular acceleration \(2~\text{rad/s}^2\) about its axis. Initially, its angular velocity is \(10~\text{rad/s}.\) In the first \(2~\text{s},\) it rotates through an angle \(\theta_{1},\), in the next \(2~\text{s} \) it rotates through an additional angle \({\theta}_{2}.\). The ratio of \(\dfrac{{{\theta}}_{2}}{{{\theta}}_{1}}\) is:
1. \(1/2\)
2. \(3/5\)
3. \(3/4\)
4. \(4/3\)
Subtopic:  Rotational Motion: Dynamics |
 52%
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The angular speed of a flywheel moving with uniform angular acceleration changes from \(1200\) rpm to \(3120\) rpm in \(16\) s. The angular acceleration in rad/s² is:
1. \(104 \pi\) 2. \(2\pi\)
3. \(4\pi\) 4. \(12\pi\)
Subtopic:  Rotational Motion: Kinematics |
 75%
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NEET - 2022
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The ratio of the moments of inertia of two spheres, about their diameters, having the same mass and their radii being in the ratio of \(1:2\), is:

1. \(2:1\) 2. \(4:1\)
3. \(1:2\) 4. \(1:4\)
Subtopic:  Moment of Inertia |
 82%
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NEET - 2022
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A string is wrapped along the rim of a wheel of the moment of inertia \(0.10~\text{kg-m}^2\) and radius \(10~\text{cm}.\) If the string is now pulled by a force of \(10~\text N,\) then the wheel starts to rotate about its axis from rest. The angular velocity of the wheel after \(2~\text s\) will be:

1. \(40~\text{rad/s}\) 2. \(80~\text{rad/s}\)
3. \(10~\text{rad/s}\) 4. \(20~\text{rad/s}\)
Subtopic:  Rotational Motion: Dynamics |
 80%
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NEET - 2022
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When a fat person tries to touch his toes (as shown in the figure), keeping the legs straight, he generally falls because of:
        
1. torque produced
2. weight
3. dizziness
4. none of these
Subtopic:  Center of Mass |
 80%
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Given below are two statements: 
Assertion (A): If polar ice melts, days will be longer.
Reason (R): Moment of inertia increases and thus angular velocity decreases.
 
1. Both (A) and (R) are true and (R) is the correct explanation of (A).
2. Both (A) and (R) are true but (R) is not the correct explanation of (A).
3. (A) is true but (R) is false.
4. Both (A) and (R) are false.
Subtopic:  Angular Momentum |
 78%
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A force is applied to a hollow spherical shell so that it acts through its centre. It causes an acceleration of \(3\) m/s2. If the same force is applied to the spherical shell, acting tangent to its surface, the acceleration will be: (Assuming no friction is available.)
1. \(3\) m/s2
2. \(2\) m/s2
3. zero
4. \(1\) m/s2
Subtopic:  Rotational Motion: Dynamics |
 56%
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A pulley of radius \(1.5~\text m\) is rotated about its axis by a force, \(F=(12t-3t^{2})~\text N\) applied tangentially (while \(t\) is measured in seconds). If the moment of inertia of the pulley about its axis of rotation is \(4.5~\text{kg-m}^2,\) the number of rotations made by the pulley before its direction of motion is reversed, will be \(\dfrac K \pi\). The value of \(K\) is:
1. \(12\) 2. \(14\)
3. \(16\) 4. \(18\)
Subtopic:  Rotational Motion: Dynamics |
 57%
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