General
✓✗A wheel is mounted on a fixed axle. A force applied tangentially at the rim produces an angular acceleration. If the same force is applied at the axle along a radius, the angular acceleration is
- zero
- double
- the same
- half
General
✓✗A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously. The ratio Kt : (Kt + Kr) for the sphere is
- 7 : 10
- 10 : 7
- 5 : 7
- 2 : 5
General
✓✗Four particles of masses 1, 2, 3 and 4 kg are placed at the corners of a square of side 1 m, in order, starting from the origin (0, 0), (1, 0), (1, 1), (0, 1). The centre of mass is at
- (0.5, 0.5) m
- (0.7, 0.5) m
- (0.4, 0.6) m
- (0.5, 0.7) m
General
✓✗The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through the point
- C, which lies between the centre and the rim
- D, which lies between the centre and the rim, closer to the centre than C
- B, which lies on the rim
- A, which is the centre
General
✓✗For a disc rolling without slipping, the ratio of rotational to translational kinetic energy is
- 2 : 1
- 2 : 5
- 1 : 2
- 1 : 1
General
✓✗Statement I: In pure rolling, the kinetic energy of the body can be written as \( \tfrac12I_P\omega^2 \), where IP is the moment of inertia about the point of contact.
Statement II: In pure rolling, the point of contact is the instantaneous axis of rotation.
Statement II: In pure rolling, the point of contact is the instantaneous axis of rotation.
- Both Statement I and Statement II are correct
- Both Statement I and Statement II are incorrect
- Statement I is correct but Statement II is incorrect
- Statement I is incorrect but Statement II is correct
General
✓✗A uniform disc of mass 4 kg and radius 0.5 m is mounted on a frictionless horizontal axle. A light string wound on it carries a 1 kg block. The block descends 2 m from rest. Its speed then is (g = 10 m s−2)
- 2 m s−1
- \( \sqrt{40} \) m s−1
- \( \sqrt{20} \) m s−1
- \( \sqrt{\dfrac{40}{3}} \) m s−1
General
✓✗The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is
- I0 + ML2/2
- I0 + ML2/4
- I0 + 2ML2
- I0 + ML2
General
✓✗The ratio of the rotational kinetic energy of a body to its angular momentum is
- \( \dfrac{\omega}{2} \)
- \( \dfrac{1}{2I} \)
- I
- 2ω
General
✓✗A uniform solid hemisphere of radius R rests with its flat face on a table. The height of its centre of mass above the table is
- \( \dfrac{3R}{8} \)
- \( \dfrac{3R}{5} \)
- \( \dfrac{4R}{3\pi} \)
- \( \dfrac{R}{2} \)
General
✓✗A dog of mass 10 kg stands on a flat boat of mass 40 kg so that it is 20 m from the shore. It walks 8 m on the boat towards the shore and stops. Neglecting friction between the boat and water, its distance from the shore is now
- 6.4 m
- 12 m
- 13.6 m
- 16 m
General
✓✗For a body rolling without slipping on a fixed surface, the frictional force
- always acts in the direction of motion
- is always kinetic friction
- does no net work on the body
- always dissipates energy as heat
General
✓✗A circular plate of radius 4R has a circular hole of radius R cut out with its centre at 2R from the centre of the plate. The centre of mass of the remaining plate is at a distance from the centre of the plate of
- \( \dfrac{2R}{5} \)
- \( \dfrac{R}{15} \)
- \( \dfrac{R}{8} \)
- \( \dfrac{2R}{15} \)
General
✓✗A diver performing somersaults tucks his body in. This
- increases his angular momentum
- reduces his angular momentum
- increases his moment of inertia
- reduces his moment of inertia and increases his angular velocity
General
✓✗A fan rotating at 300 rpm is switched off and stops after 75 revolutions. The angular retardation (assumed uniform) is
- \( \dfrac{2\pi}{3} \) rad/s2
- 2π rad/s2
- \( \dfrac{\pi}{3} \) rad/s2
- π rad/s2