A satellite is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01 R. The period of second satellite is longer than the first one (approximately) by

• 1.5 %

• 0.5 %

• 3 %

• 1 %

The change in potential energy when a body of mass m is raised to a height nR from earth's surface is (R = radius of the earth)

• $\mathrm{mgR} \frac{\mathrm{n}}{\left(\mathrm{n} - 1\right)}$

• mgR

• $\mathrm{mgR} \frac{\mathrm{n}}{\left(\mathrm{n} + 1\right)}$

• $\mathrm{mgR} \frac{{\mathrm{n}}^2}{\left({\mathrm{n}}^{2 }+ 1\right)}$

The escape velocity of body on the surface of earth is 11.2 km/s. If the mass of the earth is doubled and its radius halved, the escape velocity becomes

• 5.6 km/s

• 11.2 km/s

• 22.4 km/s

• 44.8 km/s

LANDSAT series of satellites move in near polar orbits at an altitude of

• 3600 km

• 3000 km

• 918 km

• 512 km

The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is v, then the escape velocity from the planet is

• $\sqrt{3} \mathrm{v}$

• $\sqrt{2} \mathrm{v}$

• v

• $\sqrt{5} \mathrm{v}$

Two planets have radii r₁ and r₂ and densities d₁ and d₂ respectvely. Then the ratio of acceleration due to gravity on them will be

• r₁d₁ : r₂d₂

• r₁d₂ : r₂d₁

• r₁²d₁ : r₂²d₂

• r₁ : r₂

Which of the following statements about the gravitational constant is true ?

• It is a force

• It has no unit

• It does not depend on the nature of the medium in which the bodies are kept

• It depends on the value of the masses

Four particles each of mass M, are located at the vertices of a square with side L. The gravitational potential due to this at the centre of the square is

• $-\sqrt{32} \frac{\mathrm{GM}}{\mathrm{L}}$

• $-\sqrt{64} \frac{\mathrm{GM}}{{\mathrm{L}}^2}$

• zero

• $\sqrt{32} \frac{\mathrm{GM}}{\mathrm{L}}$

59.

Two identical solid copper spheres of radius R are placed in contact with each other. The gravitational attraction between them is proportional to

• R²

• R^-2

• R⁴

• R^-4

Acceleration due to gravity is g on the surface of the earth. Then the value of the acceleration due to gravity at a height of 32 km above earth's surface is : (Assume radius of earth to be 6400 km)

• 0.99 g

• 0.8 g

• 1.01 g

• 0.9 g