If a body is moving in a circular path with decreasing speed, then: (symbols have their usual meanings):
1.
2.
3.
4. All of these
A solid sphere of mass \(M\) and radius \(R\) is in pure rolling with angular speed on a horizontal plane as shown.
The magnitude of the angular momentum of the sphere about the origin \(O\) is:
1.
2.
3.
4.
Two particles of mass, \(2\) kg and \(4\) kg, are projected from the top of a tower simultaneously, such that \(2\) kg of mass is projected with a speed \(20\) m/s at an angle \(30^{\circ}\) above horizontal and \(4\) kg is projected at \(40\) m/s horizontally. The acceleration of the centre of mass of the system of two particles will be:
1. \(\dfrac{g}{2}\)
2. \(\dfrac{g}{4}\)
3. \(g\)
4. \(2g\)
Two particles of masses \(2\) kg and \(3\) kg start to move towards each other due to mutual forces of attraction. The speed of the first particle is \(v_1\) and that of the second is \(v_2\) at a certain instant. The speed of the centre of mass is:
1. | \({v_1 + v_2} \over 2\) | 2. | \({2v_1 + 3v_2} \over 5\) |
3. | \({3v_1 + 2v_2} \over 5\) | 4. | zero |
1. | \(100\) | 2. | \(50\) |
3. | \(40\) | 4. | \(20\) |
A boy is standing on a disc rotating about the vertical axis passing through its centre. He pulls his arms towards himself, reducing his moment of inertia by a factor of m. The new angular speed of the disc becomes double its initial value. If the moment of inertia of the boy is I0 , then the moment of inertia of the disc will be:
1.
2.
3.
4.
Four masses are joined to light circular frames as shown in the figure. The radius of gyration of this system about an axis passing through the center of the circular frame and perpendicular to its plane would be: (where 'a' is the radius of the circle)
1.
2.
3. a
4. 2a
Five particles of mass \(2\) kg each are attached to the circumference of a circular disc of a radius of \(0.1\) m and negligible mass. The moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane will be:
1. \(1\) kg-m2
2. \(0.1\) kg-m2
3. \(2\) kg-m2
4. \(0.2\) kg-m2
A uniform rod of length l is hinged at one end and is free to rotate in the vertical plane. The rod is released from its position, making an angle with the vertical. The acceleration of the free end of the rod at the instant it is released is:
1. | \(\frac{3 g \sin \theta}{4} \) | 2. | \(\frac{3 g \cos \theta}{2} \) |
3. | \(\frac{3 g \sin \theta}{2} \) | 4. | \(\frac{3 g \cos \theta}{4}\) |