Q. No.A wheel is rotating about an axis through its centre at \(720~\text{rpm}.\) It is acted upon by a constant torque opposing its motion for \(8\) seconds to bring it to rest finally.
The value of torque in \((\text{N-m })\) is:
(given \(I=\frac{24}{\pi}~\text{kg.m}^2)\)
1. \(48\)
2. \(72\)
3. \(96\)
4. \(120\)
(given \(I=\frac{24}{\pi}~\text{kg.m}^2)\)
1. \(48\)
2. \(72\)
3. \(96\)
4. \(120\)
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 force \(- F \hat k\) acts on point \(O\) the origin of the coordinate system. What is the torque about the point \((1,-1)\)?
1. \(-F(\hat i + \hat j)\)
2. \(F(\hat i + \hat j)\)
3. \(-F(\hat i -\hat j)\)
4. \(F(\hat i - \hat j)\)
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. |
A particle of mass \(m\) moves in the\(XY\) plane with a velocity of \(v\) along the straight line \(AB.\) If the angular momentum of the particle about the origin \(O\) is \(L_A\) when it is at \(A\) and \(L_B\) when it is at \(B,\) then:
| 1. | \(L_A>L_B\) |
| 2. | \(L_A=L_B\) |
| 3. | The relationship between \(L_A\) and \(L_B\) depends upon the slope of the line \(AB.\) |
| 4. | \(L_A<L_B\) |
A wheel with a radius of \(20\) cm has forces applied to it as shown in the figure. The torque produced by the forces of \(4\) N at \(A\), \(8~\)N at \(B\), \(6\) N at \(C\), and \(9~\)N at \(D\), at the angles indicated, is:
1. \(5.4\) N-m anticlockwise
2. \(1.80\) N-m clockwise
3. \(2.0\) N-m clockwise
4. \(3.6\) N-m clockwise
If the radius of the earth is suddenly contracted to half of its present value, then the duration of the day will be of:
| 1. | 6 hours | 2. | 12 hours |
| 3. | 18 hours | 4. | 24 hours |
| 1. | \(\dfrac{7}{3}~\text{m}\) | 2. | \(\dfrac{10}{7}~\text{m}\) |
| 3. | \(\dfrac{12}{7}~\text{m}\) | 4. | \(\dfrac{9}{7}~\text{m}\) |
The centre of the mass of \(3\) particles, \(10~\text{kg},\) \(20~\text{kg},\) and \(30~\text{kg},\) is at \((0,0,0).\) Where should a particle with a mass of \(40~\text{kg}\) be placed so that its combined centre of mass is \((3,3,3)?\)
1. \((0,0,0)\)
2. \((7.5, 7.5, 7.5)\)
3. \((1,2,3)\)
4. \((4,4,4)\)
© 2026 GoodEd Technologies Pvt. Ltd.