Consider the following hypothetical case. A planet has the mass equal to half the mass of the earth and its radius is twice the radius of earth. What is the acceleration due to gravity of the given planet ?
A)1.225 m/s^2
B)2.45 m/s^2
C)19.6 m/s^2
D)39.2 m/s^2

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Solution

Dear Student,
$A c c e l e r a t i o n d u e t o g r a v i t y, g = G \frac{M}{R^{2}} = 9.8 m s^{- 2} w h e r e, G = G r a v i t a t i o n a l C o n s \tan t M = m a s s o f e a r t h R = R a d i u s o f t h e e a r t h G i v e n, M a s s o f t h e p l a n e t, M' = \frac{M}{2} R a d i u s o f t h e p l a n e t, R' = 2 R A c c e l e r a t i o n d u e t o g r a v i t y o f t h e p l a n e t, g' = G \frac{M'}{R'^{2}} = G \frac{M}{2} \times \frac{1}{{(2 R)}^{2}} = \frac{1}{8} G \frac{M}{R^{2}} = \frac{g}{8} = \frac{9.8}{8} = 1.225 m s^{- 2}$
Ans (A)

Regards

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