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A mass ‘\(m\)’ is supported by a massless string wound around a uniform hollow cylinder of mass \(m\) and radius \(R\). If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

                              
1. \(\frac{g}{2}\)
2. \(\frac{5g}{6}\)
3. \(g\)
4. \(\frac{2g}{3}\)

Q1:
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Subtopic:  Rotational Motion: Dynamics |
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Suppose that the angular velocity of the rotation of the earth is increased. Then as a consequence:
1. Weight of the objects everywhere on the earth will decrease
2. Weight of the objects everywhere on the earth will increase
3. Except at the poles weight of the object on the earth will decrease 
4. There will be no change in weight anywhere on the earth.
Q2:
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Subtopic:  Rotational Motion: Dynamics |
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A uniform disc with mass \(M=4\) kg and radius \(R=10\) cm is mounted on a fixed horizontal axle as shown in the figure. A block with mass \(m=2\) kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is:  (Take \(g=10\) ms–2)
     
1. \(12\) N
2. \(20\) N
3. \(10\) N
4. \(15\) N
Q3:
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Subtopic:  Rotational Motion: Dynamics |
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A disc of mass \(1\) kg and radius \(R\) is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of the disc. A body of the same mass as that of the disc is fixed at the highest point of the disc. Now the system is released. When the body comes to the lowest position, its angular speed will be: (take \(g=10~\text{ms}^{-2}\))
1. \(4 \sqrt{\dfrac{{5}}{3{R}}} ~ \text {rad/s}\)
2. \(4 \sqrt{\dfrac{{4}}{3{R}}} ~ \text {rad/s}\)
3. \(4 \sqrt{\dfrac{1}{R}} ~ \text{rad/s}\)
4. \(4 \sqrt{\dfrac{1}{3R}} ~ \text{rad/s}\)
Q4:
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Subtopic:  Rotational Motion: Dynamics |
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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. \(18\)
Q5:
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Subtopic:  Rotational Motion: Dynamics |
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 A solid cylinder is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding, for the strings to achieve a speed of \(4~\text{ms}^{-1},\) is:
(take \(g=10~\text{ms}^{-2}\) )
       

1. \(100~\text{cm}\)
2. \(110~\text{cm}\)
3. \(120~\text{cm}\)
4. \(130~\text{cm}\)
Q6:
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Subtopic:  Rotational Motion: Dynamics |
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A force of \(54.4~\text{N}\) is applied on the free end of a string wrapped around a solid cylinder of mass \(15~\text{kg}\) and radius \(10~\text{cm}.\) What is the angular acceleration of the cylinder?
1. \(94.10\) rad/s2 2. \(72.5\) rad/s2
3. \(14.50\) rad/s2 4. \(94.50\) rad/s2
Q7:
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Subtopic:  Rotational Motion: Dynamics |
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