Forum

Gravitation

Let the speed of the planet

at the perihelion P in Fig. 7.1(a) be vP and

the Sun-planet distance SP be rP. Relate

{rP, vP} to the corresponding quantities at

the aphelion {rA, vA}. Will the planet take

equal times to traverse BAC and CPB ?

Gravitation

Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart ona horizontal table. What is the gravitational force and potential at the mid point ofthe line joining the centres of the spheres ? Is an object placed at that point inequilibrium? If so, is the equilibrium stable or unstable ?

Gravitation

Two stars each of one solar mass (= 2×1030 kg) are approaching each other for a

head on collision. When they are a distance 109

 km, their speeds are negligible.

What is the speed with which they collide ? The radius of each star is 104

 km.

Assume the stars to remain undistorted until they collide. (Use the known value

of G).

Gravitation

A satellite orbits the earth at a height of 400 km above the surface. How much

energy must be expended to rocket the satellite out of the earth’s gravitational

influence? Mass of the satellite = 200 kg; mass of the earth = 6.0×1024 kg; radius of

the earth = 6.4 × 106

 m; G = 6.67 × 10–11 N m2 kg–2

.

Gravitation

The escape speed of a projectile on the earth’s surface is 11.2 km s–1. A body is
projected out with thrice this speed. What is the speed of the body far away from
the earth? Ignore the presence of the sun and other planets.

Gravitation

A rocket is fired vertically with a speed of 5 km s-1 from the earth’s surface. How far
from the earth does the rocket go before returning to the earth ? Mass of the earth
= 6.0 × 1024 kg; mean radius of the earth = 6.4 × 106
m; G = 6.67 × 10–11 N m2 kg–2

Gravitation

Assuming the earth to be a sphere of uniform mass density, how much would a
body weigh half way down to the centre of the earth if it weighed 250 N on the
surface ?

Gravitation

A body weighs 63 N on the surface of the earth. What is the gravitational force on it
due to the earth at a height equal to half the radius of the earth ?

Gravitation

A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the
earth is 1.50 × 108
km away from the sun ?

Gravitation

How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of
the earth around the sun is 1.5 × 108
km.