1. | \(9.9\) m | 2. | \(10.1\) m |
3. | \(10\) m | 4. | \(20\) m |
The one-quarter sector is cut from a uniform circular disc of radius \(R\). This sector has a mass \(M\). It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation will be:
1. | \(\frac{1}{2} M R^2 \) | 2. | \(\frac{1}{4} M R^2 \) |
3. | \(\frac{1}{8} M R^2 \) | 4. | \(\sqrt{2} M R^2\) |
A billiard ball of mass m and radius r, when hit in a horizontal direction by a cue at a height h above its centre, acquires a linear velocity . The angular velocity acquired by the ball will be:
1.
2.
3.
4.
A ladder is leaned against a smooth wall and it is allowed to slip on a frictionless floor. Which figure represents the path followed by its center of mass?
1. | |
2. | |
3. | 4. |
A circular platform is mounted on a frictionless vertical axle. Its radius is R = 2m and its moment of inertia about the axle is 200 kg m2. Initially, it is at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at a speed of 1 m s–1 relative to the ground. The time taken by the man to complete one revolution is:
1.
2.
3.
4.
When a mass is rotating in a plane about a fixed point, its angular momentum is directed along:
1. | a line perpendicular to the plane of rotation |
2. | the line making an angle of \(45^\circ\) to the plane of rotation |
3. | the radius |
4. | the tangent to the orbit |
Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D has a 2 kg mass, 0.2 m radius, and an initial angular velocity of 50 rad s. Disc D has 4 kg mass, 0.1 m radius, and initial angular velocity of 200 rad s. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad.s) of the system will be:
1. 60
2. 100
3. 120
4. 40
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. \(2g\)