Two satellites of earth S₁ and S₂, are moving in the same orbit. The mass of S₁ is four times the mass of S₂. Which one of the following statement is true?

• The time period of S₁ is four times that of S₂

• The potential energies of earth and satellite in the two cases are equal 

• S₁ and S₂ are moving with the same speed

• S₁ and S₂ are moving with the same speed

The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is fv_e, where v_e is its escape velocity from the surface of the earth. The value of f is

Two bodies, A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is

• 5/4

• 12/5

• 5/12

• 5/12

Suppose the charge of a proton and an electron differ slightly. One of them is –e, the other is (e + Δe). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of [Given mass of hydrogen
mh = 1.67 × 10^–27 kg]

• 10^–20 C

• 10^–23 C

• 10^–37 C

• 10^–37 C

The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then

• d =1/2 km

• d = 1 km

• d =3/2 km

• d =3/2 km

Which of the following statements is correct?
(a) Centre of the mass of a body always coincides with the centre of gravity of the body.
(b) Centre of the mass of a body is the point at which the total gravitational torque on the body is zero
(c) A couple on a body produce both translational and rotational motion in a body.
(d) Mechanical advantage greater than one means that small effort can be used to lift a large load.

• (b) and (d)

• (a) and (b)

• (b) and (c)

• (b) and (c)

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:

• Keep floating at the same distance between them

• Move towards each other

• Move away from each other

• Move away from each other

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?

• Raindrops will fall faster

• Walking on the ground would become more difficult

• 'g' on the Earth will not change

• Time period of a simple pendulum on the Earth would decrease

Two 20 g flatworms climb over a very thin wall, 10 cm high. One of the worms is 20 cm long, the other is wider and only 10 cm long. which of the following statement is correct regarding them?

• 20 cm worm has done more work against gravity

• 10 cm worm has done more work against gravity

• Both worms have done equal work against gravity

• Ratio of work done by both the worms is 4:5

A rocket is intended to leave the Earth's gravitational field. The fuel in its main engine is a little less than the amount that is necessary and an auxiliary engine, (only capable of operating for a short time) has to be used as well. When is it best to switch on the auxiliary engine?

• at take-off

• When the rocket has nearly stopped with respect to the Earth

• It doesn't matter

• Can't say