Q. No.1. \(5:2\)
2. \(3:5\)
3. \(5:3\)
4. \(2:5\)
1. \(2v\)
2. zero
3. \(v\)
4. \(4v\)
1. \(1~\text{rad/s}\)
2. \(5~\text{rad/s}\)
3. \(10~\text{rad/s}\)
4. \(15~\text{rad/s}\)
| 1. | \(5~ \text m\) | 2. | \(\dfrac{10}{3} \mathrm{~m}\) |
| 3. | \(\dfrac{20}{3} \mathrm{~m}\) | 4. | \(10~ \text m\) |
| 1. | \(104 \pi\) | 2. | \(2\pi\) |
| 3. | \(4\pi\) | 4. | \(12\pi\) |
| 1. | \(1:\sqrt{2}\) | 2. | \(2:1\) |
| 3. | \(\sqrt{2}:1\) | 4. | \(4:1\) |
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. | \(1:4\) |
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. | \(20~\text{rad/s}\) |
| 1. | \(0.7~\text{kg-m}^2\) | 2. | \(3.22~\text{kg-m}^2\) |
| 3. | \(30.8~\text{kg-m}^2\) | 4. | \(0.07~\text{kg-m}^2\) |
From a circular ring of mass \({M}\) and radius \(R,\) an arc corresponding to a \(90^\circ\) sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is \(K\) times \(MR^2.\) The value of \(K\) will be:
| 1. | \(\frac{1}{4}\) | 2. | \(\frac{1}{8}\) |
| 3. | \(\frac{3}{4}\) | 4. | \(\frac{7}{8}\) |
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