Q. No.A small mass attached to a string rotates on a frictionless table top as shown. If the tension on the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of \(2,\) the kinetic energy of the mass will
| 1. | Increase by a factor of \(4\) |
| 2. | Decrease by a factor of \(2\) |
| 3. | Remain constant |
| 4. | Increase by a factor of \(2\) |
A solid sphere is rotating about a diameter at an angular velocity \(w.\) If it cools so that its radius reduces to\(\frac1n\) of its original value, its angular velocity becomes
1. \(\frac wn\)
2. \(\frac{w}{{n}^2}\)
3. \(nw\)
4. \(n^2w\)
A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass 'm' is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period
1. Decreases continuously
2. Decreases initially and increases again
3. Remains unaltered
4. Increases continuously
Given below are two statements:
| Assertion (A): | The speed of whirlwind in a tornado is alarmingly high. |
| Reason (R): | If no external torque acts on a body, its angular velocity remains conserved. |
| 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. |
A particle of mass 2 kg located at the position m has a velocity of 2 m/s. Its angular momentum about z-axis in kg- is :
1. +4
2. +8
3. -4
4. -8
In an orbital motion, the angular momentum vector is
1. Along the radius vector
2. Parallel to the linear momentum
3. In the orbital plane
4. Perpendicular to the orbital plane
A particle of mass \(m\) moves with a constant velocity along \(3\) different paths, \(DE, OA\) and \(BC\). Which of the following statements is not correct about its angular momentum about point \(O\)?
| 1. | It is zero when it is at \(A\) and moving along \(OA\). |
| 2. | The same at all points along the line \(DE\). |
| 3. | Of the same magnitude but oppositely directed at \(B\) and \(D\). |
| 4. | Increases as it moves along the line \(BC\). |
A bob of mass m attached to an inextensible string of length l is suspended from vertical support. The bob rotates in a horizontal circle with an angular speed about the vertical. About the point of suspension.
| 1. | Angular momentum is conserved |
| 2. | Angular momentum changes in magnitude but not in the direction |
| 3. | Angular momentum changes in direction but not in magnitude |
| 4. | Angular momentum changes both in direction and magnitude |
A thin uniform circular disc of mass \(M\) and radius \(R\) is rotating in a horizontal plane about an axis passing through its center and perpendicular to its plane with an angular velocity . Another disc of the same dimensions but of mass \(\frac{1}{4}M\) is placed gently on the first disc co-axially. The angular velocity of the system will be:
| 1. | 2. | ||
| 3. | 4. |
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