Question

If the mass of a planet is four times the mass of the earth and the radius is half of the earth, then the gravitational acceleration of the planet is:
1. 16g
2. g/16
3. 4g
4. g

Answer 1

Correct Answer - Option 1 : 16g

CONCEPT:

Acceleration Due to Gravity:

• The force of attraction exerted by the earth on a body is called gravitational pull or gravity.
• We know that when a force acts on a body, it produces acceleration. Therefore, a body under the effect of gravitational pull must accelerate.
• The acceleration produced in the motion of a body under the effect of gravity is called acceleration due to gravity, it is denoted by g.
• The acceleration due to gravity on the surface of the earth is given by,

\(g = \frac{{GM}}{{{R^2}}}\)

Where G = universal gravitational constant, M = mass of the earth, and R = radius of the earth​

CALCULATION:

When M_P = 4M and \(R_P=\frac{R}{2}\)

• The gravitational acceleration of the earth is given as,

\(⇒ g = \frac{{GM}}{{{R^2}}}\)     ------ (1)

• The gravitational acceleration of the planet is given as,

\(⇒ g_{P} = \frac{{GM_{P}}}{{{R_{P}^2}}}\)

\(⇒ g_{P} = \frac{{G\times4M}}{{{(\frac{R}{2})^2}}}\)

\(⇒ g_{P} = \frac{{16\,GM}}{{{R^2}}}\)     -----(2)

By equation 1 and equation 2,

⇒ g_P = 16g

• Hence, option 1 is correct.