If a_r and a_t represent radial and tangential accelerations, the motion of a particle will be uniformly circular if :

• a_r = 0 and a_t = 0

• a_r = 0 and a_t ≠ 0

• a_r ≠ 0 and a_t = 0

• a_r ≠ 0 and a_t ≠ 0

The radius of orbit of satellite of earth is R. Its kinetic energy is proportional to :

• $\frac{1}{\mathrm{R}}$

• $\frac{1}{\sqrt{\mathrm{R}}}$

• R

• $\frac{1}{{\mathrm{R}}^{3/2}}$

A cone filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down. What must be the maximum period of revolution?

• 2 sec

• 4 sec

• 1 sec

• 6 sec

4.

The length, breadth and thickness of a block are given by l = 12 cm, b = 6 cm and t = 2.45 cm. The volume of the block according to the idea of significant figures should be:

• 1 × 10² cm³

• 2 × 10² cm³

• 1.763 × 10² cm³

• none of the above

Five particles of mass 2 kg are attached to the rim of a circular disc of radius 0.1 m and negligible mass. Moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane is

• 1 kg m²

• 0.1 kg m²

• 2 kg m²

• 0.2 kg m²

A sphere of diameter 0.2 m and mass 2 kg is rolling on an inclined plane with velocity v = 0.5 m/s. The kinetic energy of the sphere is :

• 0.1 J

• 0.3 J

• 0.5 J

• 0.42 J

A police jeep is chasing with a velocity of 45 km/h, a thief in another jeep moving with velocity 153 km/h. Police fire a bullet with muzzle velocity of 180 m/s. The velocity with which it will strike the car of the thief is :

• 150 m/s

• 27 m/s

• 450 m/s

• 250 m/s

The dimensional formula for Young's modulus is

• [ML^-1T^-2]

• [M⁰LT^-2]

• [MLT^-2]

• [ML²T^-2]

The radius of orbit of a planet is two times that of the earth. The time period of the planet is :

• 4.2 T

• 2.8 T

• 5.6 T

• 8.4 T

A body falls from a height h = 200 m. The ratio of distance travelled in each 2 sec, during t = 0 to t = 6 second of the journey is

• 1 : 4 : 9

• 1 : 2 : 4

• 1 : 3 : 5

• 1 : 2 : 3