question_answer

The density of newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be: [AIPMT (S) 2004]

A) \[2\,R\]

B) \[4\,R\]

C) \[\frac{1}{4}R\]

D) \[\frac{1}{2}R\]

Correct Answer: D

Solution :

Key Idea: Acceleration due to gravity is the acceleration in vertically downward direction acting on every object on earth. Its value is given by Newton's second law which is

The acceleration due to gravity on an object of mass m

but from Newton's law of gravitation

where M is the mass of the earth and R the radius of earth.

Given:

Also,

or

or

or

or