Q. No.A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (Sphere/cylinder) will be:
1. 2:3
2. 1:5
3. 1:4
4. 3:1
| 1. | \(\dfrac{8 \pi}{3}~\text{rad/s}^2 \) | 2. | \(\dfrac{4 \pi}{3}~\text{rad/s}^2 \) |
| 3. | \(\dfrac{8}{3}~\text{rad/s}^2 \) | 4. | \(\dfrac{4}{3}~\text{rad/s}^2 \) |
| 1. | \(20~\text{rad/s}\) | 2. | \(15~\text{rad/s}\) |
| 3. | \(10~\text{rad/s}\) | 4. | \(2~\text{rad/s}\) |
| 1. | \(4~\text{rad/s}\) | 2. | \(5~\text{rad/s}\) |
| 3. | \(8~\text{rad/s}\) | 4. | \(10~\text{rad/s}\) |
1. \(3\)
2. \(7\)
3. \(9\)
4. \(5\)
The moment of inertia of a body about a given axis is \(1.5\text{ kg.m}^2.\) Initially, the body is at rest. In order to produce rotational kinetic energy of \(1200\text{ J},\) the angular acceleration of \(20\text{ rad/s}^2\) must be applied about the axis for a duration of:
| 1. | \(5\text{ s}\) | 2. | \(3\text{ s}\) |
| 3. | \(2.5\text{ s}\) | 4. | \(2\text{ s}\) |
\(\alpha=(6 {t}^2-2 {t}),\)
where \(t\) is in seconds.
At \(t=0,\) the ball has an angular velocity of \(10\) rad/s and an angular position of \(4\) rad. Which of the following expressions correctly represents the angular position \(\theta({t})\) of the ball?
| 1. | \( \dfrac{3}{2} t^4-t^2+10 t \) | 2. | \(\dfrac{t^4}{2}-\dfrac{t^3}{3}+10 t+4 \) |
| 3. | \( \dfrac{2 t^4}{3}-\dfrac{t^3}{6}+10 t+12 \) | 4. | \( 2 t^4-\dfrac{t^3}{2}+5 t+4 \) |
1. \(14~\text{rad}\)
2. \(24~\text{rad}\)
3. \(40~\text{rad}\)
4. \(56~\text{rad}\)
1. \(50\)
2. \(100\)
3. \(150\)
4. \(200\)
A solid sphere of mass \(m\) and radius \(R\) is rotating about its diameter. A solid cylinder of the same mass and the same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (sphere/cylinder) will be:
| 1. | \(2:3\) | 2. | \(1:5\) |
| 3. | \(1:4\) | 4. | \(3:1\) |
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