General
✓✗Kepler's second law (equal areas in equal times) is a consequence of the conservation of
- mass
- angular momentum
- linear momentum
- energy
General
✓✗A uniform rectangular plate of mass M and sides a and b. Its moment of inertia about an axis through its centre perpendicular to its plane is
- \( \dfrac{M(a^2 + b^2)}{3} \)
- \( \dfrac{M(a + b)^2}{12} \)
- \( \dfrac{M(a^2 + b^2)}{12} \)
- \( \dfrac{Mab}{12} \)
General
✓✗Which of the following bodies has its centre of mass outside the material of the body?
- A uniform rod
- A solid sphere
- A solid cube
- A circular ring
General
✓✗Match List I with List II (analogous quantities in linear and rotational motion).
| List I | List II |
| P. Mass | 1. Torque |
| Q. Force | 2. Angular momentum |
| R. Linear momentum | 3. Moment of inertia |
| S. Power Fv | 4. \( \tau\omega \) |
- P-1, Q-3, R-2, S-4
- P-3, Q-1, R-2, S-4
- P-3, Q-2, R-1, S-4
- P-2, Q-1, R-3, S-4
General
✓✗The moment of inertia of a uniform disc of mass M and radius R about its axis is
- \( \dfrac25MR^2 \)
- \( \dfrac12MR^2 \)
- MR2
- \( \dfrac14MR^2 \)
General
✓✗A ring and a disc of the same mass roll without slipping with the same linear speed. The ratio of their total kinetic energies (ring : disc) is
- 2 : 1
- 1 : 1
- 4 : 3
- 3 : 4
General
✓✗A cylinder is pulled along a rough horizontal floor by a horizontal force F applied at its centre, so that it rolls without slipping. The acceleration of a solid cylinder of mass m is
- \( \dfrac{F}{2m} \)
- \( \dfrac{F}{3m} \)
- \( \dfrac{2F}{3m} \)
- \( \dfrac Fm \)
General
✓✗The moment of inertia of a body about a given axis is 1.2 kg m2. Initially the body is at rest. In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 rad/s2 must be applied about that axis for a duration of
- 2 s
- 4 s
- 10 s
- 8 s
General
✓✗A yo-yo (a uniform disc of mass m and radius R) falls with its string unwinding, the upper end of the string being held fixed. The tension in the string is
- \( \dfrac{mg}{2} \)
- mg
- \( \dfrac{2mg}{3} \)
- \( \dfrac{mg}{3} \)
General
✓✗The centre of gravity of a body coincides with its centre of mass when
- the body is a sphere only
- the body is in motion
- the gravitational field is uniform over the body
- the body is very large
General
✓✗The dimensional formula of angular momentum is the same as that of
- Planck's constant
- energy
- power
- torque
General
✓✗If I is the moment of inertia of a uniform ring about its axis, its moment of inertia about a tangent perpendicular to its plane is
- 3I
- 2I
- \( \dfrac32I \)
- I
General
✓✗The moment of inertia of a thin ring of mass M and radius R about its axis (perpendicular to its plane through its centre) is
- 2MR2
- \( \dfrac25MR^2 \)
- MR2
- \( \dfrac12MR^2 \)
General
✓✗Consider a contact point P of a wheel on the ground, which rolls on the ground without slipping. The value of the displacement of point P when the wheel completes half a rotation (radius of wheel 1 m) is
- 2 m
- \( \sqrt{\pi^2 + 4} \) m
- π m
- \( \sqrt{\pi^2 + 2} \) m
General
✓✗The moment of inertia of a uniform cylinder of mass M, length L and radius R about an axis through its centre perpendicular to its length is
- \( \dfrac{MR^2}{2} \)
- \( M\left(\dfrac{R^2}{2} + \dfrac{L^2}{12}\right) \)
- \( \dfrac{ML^2}{12} \)
- \( M\left(\dfrac{R^2}{4} + \dfrac{L^2}{12}\right) \)