The linear momentum and position vector of the planet is perpendicular to each other at

(a)

perihelion and aphelion

(b)

at all points

(c)

only at perihelion

(d)

no point

If the masses of the Earth and Sun suddenly double, the gravitational force between them will

(a)

remain the same

(b)

increase 2 times

(c)

increase 4 times

(d)

decrease 2 times

A planet moving along an elliptical orbit is closest to the Sun at distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are linear speeds at these points respectively. Then the ratio \({v_1\over v_2}\) is

(a)

\({r_2\over r_1}\)

(b)

\(({r_2\over r_1})^2\)

(c)

\({r_1\over r_2}\)

(d)

\(({r_1\over r_2})^2\)

According to Kepler’s second law, the radial vector to a planet from the Sun sweeps out equal areas in equal intervals of time. This law is a consequence of

(a)

conservation of linear momentum

(b)

conservation of angular momentum

(c)

conservation of energy

(d)

conservation of kinetic energy

The gravitational potential energy of the Moon with respect to Earth is

(a)

always positive

(b)

always negative

(c)

can be positive or negative

(d)

always zero

Acceleration to Kepler's second law the radius vector of a planet sweeps out equal areas in equal intervals of fire. The law is consequence of conservations of _______________.

(a)

linear momentum

(b)

angular momentum

(c)

energy

(d)

Newton's law of gravitation

 

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 _____________.

(a)

4:1

(b)

1:8

(c)

8:1

(d)

1:4

Two practicals of equal mass m go round a circle of radius R under the action of their mutual gravitational attraction the speed of each particle is ___________.

(a)

\(\frac { 1 }{ 2R } \sqrt { \frac { 1 }{ Gm } } \)

(b)

\(\frac { Gm }{ 2R } \)

(c)

\(\frac { 1 }{ 2 } \sqrt { \frac { GM }{ R } } \)

(d)

\(\sqrt { \frac { 4GM }{ R } } \)

A body projected electrically from the earth reaches a height equal to earth's radius before returning to the earth: The power exerted by the gravitational force is greatest ____________.

(a)

at the highest position of the body

(b)

at the instant just before the body hits the earth

(c)

it remains constant all through

(d)

at the instant just after the body is projected

A rocket is fired from the earth. The body is projected the distance between the earth of the moon is r & the mass of the earth is 81 times the mass of the moon. The gravitational force on the rocket will be zero, when its from the moon is ______________.

(a)

\(\frac { r }{ 5 } \)

(b)

\(\frac { r }{ 10 } \)

(c)

\(\frac { r }{ 15 } \)

(d)

\(\frac { r }{ 20 } \)