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}}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

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 s

• 4 s

• 1 s

• 6 s

The maximum range of a gun on horizontal terrain is 16 km if g=10m/s^2. What must be the muzzle velocity of the shell?

• 200 m/s

• 100 m/s

• 400 m/s

• 300 m/s

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

• 1.76 × 10² cm³

• None of these

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 particle is kept at rest at the top of a sphere of diameter 42 m. When disturbed slightly, it slides down. At what height h from the bottom, the particle will leave the sphere?

• 14 m

• 28 m

• 35 m

• 7 m

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

• 150 m/s

• 27 m/s

• 450 m/s

• 250 m/s

A simple pendulum of length l has a maximum angular displacement θ. The maximum kinetic energy of the bob is

• mgl (1-cosθ)

• 0.5 mgl

• mgl

• 0.5 mgl

The radius R of the soap bubble is doubled under isothermal condition. If T be the surface tension of soap bubble. The work done in doing so is given by

• $32 {\mathrm{\pi R}}^2\mathrm{T}$

• $24 {\mathrm{\pi R}}^2\mathrm{T}$

• $8 {\mathrm{\pi R}}^2\mathrm{T}$

• $4 {\mathrm{\pi R}}^2\mathrm{T}$

A body of specific heat 0.2 kcal/ kg° C is heated through 100°C. The percentage increase in its mass is

• 9%

• 9.3×10^-11 %

• 10%

• None of these