A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 4R. The ratio of their respective periods is

• 4 : 1

• 1 : 8

• 8 : 1

• 1 : 4

A body is projected with a velocity of 2 x 11.2 kms^-1 from the surface of earth. The velocity of the body when it escapes the gravitational pull of earth is

• $\sqrt{3} \times 11.2 {\mathrm{kms}}^{-1}$

• 11.2 kms^-1

• $\sqrt{2} \times 11.2 {\mathrm{kms}}^{-1}$

• 6.5 × 11.2 kms^-1

If the escape velocity of a planet is 3 times that of the earth and its radius is 4 times that of the earth, then the mass of the planet is (Mass of the earth = 6 x 10²⁴ kg)

• 1.62 × 10²² Kg

• 0.72 × 10²² kg

• 2.16 × 10²⁶ kg

• 1.22 × 10²² kg

44.

The total energy of a circularly orbiting satellite is

• twice the kinetic energy of the satellite

• half the kinetic energy of the satellite

• half the potential energy of the satellite

• equal to the potential energy of the satellite

If an earth satellite of mass m orbiting at a distance 2R from the centre of earth has to be transferred into the orbit of radius 3 R, the amount of energy required is (R = radius of earth)

• mgR

• $\frac{\mathrm{mgR}}{3}$

• $\frac{\mathrm{mgR}}{2}$

• $\frac{\mathrm{mgR}}{12}$

The ratio of radii of earth to another planet is $\frac{2}{3}$and the ratio of their mean densities is $\frac{4}{5}$. If an astronaut can jump to a maximum height of 1.5 m on the earth, with the same effort, the maximum height he can jump on the planet is

• 1 m

• 0.8 m

• 0.5 m

• 1.25 m

At what depth below the surface of the earth, the value of g is the same as that at a height of 5 km ?

• 1.25 km

• 2.5 km

• 10 km

• 7.5 km

Infinite number of masses, each 1 kg, are placed along the x-axis at x = ± 1m, ± 2 m, ± 4 m, ± 8 m, ±16m. The magnitude of the resultant gravitational potential in terms of gravitational constant G at the origin (x = 0) is

• G/2

• G

• 2G

• 4G

Three identical bodies of mass M are located at the vertices of an equilateral triangle of side L. They revolve under the effect of mutual gravitational force in a circular orbit, circumscribing the triangle while preserving the equilateral triangle. Their orbital velocity is

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

• $\sqrt{\frac{3\mathrm{GM}}{2\mathrm{L}}}$

• $\sqrt{\frac{3\mathrm{GM}}{\mathrm{L}}}$

• $\sqrt{\frac{2\mathrm{GM}}{3\mathrm{L}}}$

A satellite is revolving around the earth with a kinetic energy E. The minimum addition of kinetic energy needed to make it escape from its orbit is

• 2E

• $\sqrt{\mathrm{E}}$

• E

• $\sqrt{\mathrm{E}}/2$