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

38.

The planets with radii R₁ and R₂ have densities ρ1, ρ2 respectively. Their atmospheric pressure is p1 and p2 respectively. Therefore, the ratio of masses of their atmospheres, neglecting variation of g within the limits of the atmosphere is

• $\frac{{\mathrm{\rho }}_1{\mathrm{R}}_2{\mathrm{\rho }}_1}{{\mathrm{\rho }}_2{\mathrm{R}}_1{\mathrm{\rho }}_2}$

• $\frac{{\mathrm{\rho }}_1{\mathrm{R}}_2{\mathrm{\rho }}_2}{{\mathrm{pP}}_2{\mathrm{R}}_1{\mathrm{\rho }}_1}$

• $\frac{{\mathrm{p}}_1{\mathrm{R}}_1{\mathrm{\rho }}_1}{{\mathrm{p}}_2{\mathrm{R}}_2{\mathrm{\rho }}_2}$

• $\frac{{\mathrm{p}}_1{\mathrm{R}}_1{\mathrm{\rho }}_2}{{\mathrm{p}}_2{\mathrm{R}}_2{\mathrm{\rho }}_1}$

A thin symmertical double convex lens of refractive index μ₂ = 1.5 is placed between a medium of refractive index μ₁ = 1.4 to the left and another medium of refractive index μ₃ = 1.6 to the right. Then, the system behaves as

• a convex lens

• a concave lens

• a glass plate

• a convexo-concave lens

The escape velocity for the earth is 11.2 km/sec. The mass of another planet 100 times mass of earth and its radius is 4 times radius of the earth. The escape velocity for the planet is

• 56.0 km/sec

• 280 km/sec

•  112 km/sec

•  56 km/sec