# CBSE Class 11-Physics: Gravitation Practice Problems (Derivation Based)

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**Question 1:**

(a) Define escape velocity. Derive expression for escape velocity of an object from the surface of planet.

(b) Does it depend on location from where it is projected?

**Question 2:**

Derive an expression for the gravitational potential energy above the surface of the earth.

**Question 3:**

If a person goes to a height equal to radius of earth from its surface, what would be his weight relative to that on the earth?

**Question 4:**

Find the height from the surface of earth at which weight of the body of mass reduced to of its weight on the surface .

**Question 5:**

Derive an expression to show that the value of acceleration due to gravity decreases with the depth.

**Question 6:**

Two bodies of mass and are placed at a distance apart. Show that the position, where the gravitational field due to them is zero, the potential is given by

**Question 7:**

Two masses and are initially at rest at infinite distance apart. They approach each other due to gravitational interaction. Find their speed of approach at the instant when they are distance apart.

**Question 8:**

Define orbital velocity and find the expression for orbital velocity of for a satellite orbiting at height above the surface of the earth.

**Question 9:**

Write a detailed note on geostationary satellites.

**Question 10:**

Suppose that gravitational force varies inversely as the nth power of distance. Then find the expression for the period of a planet in a circular orbit of radius .

**Question 11:**

If is the period of the satellite revolving just above the surface of a planet, whose average density is ρ, show that is a universal constant.

**Question 12:**

A particle is projected vertically upwards from the surface of earth (radius R) with a kinetic energy equal to half of the minimum value needed for it to escape. Find the height to which it rises above the surface of earth.