Question

The density of a planet is three times that of earth and radius \(2.5\) times that of earth. If \(g_p\) and \(g_e\) represents acceleration due to gravity on planet and earth respectively then ratio \(g_p\) to \(g_e\) is

• A. \(7.5\)
• B. \(3.5\)
• C. \(6.5\)
• D. \(9.5\)

Hint:

g is proportional to density times radius.

Answer 1

The Correct Option is A

Step 1: Compute mass ratio first:
$\dfrac{M_p}{M_e}=\dfrac{\rho_p}{\rho_e}\left(\dfrac{R_p}{R_e}\right)^3=3\times(2.5)^3=3\times15.625=46.875$.

Step 2: Compute g ratio:
$\dfrac{g_p}{g_e}=\dfrac{M_p}{M_e}\left(\dfrac{R_e}{R_p}\right)^2=\dfrac{46.875}{6.25}=7.5$.

Step 3: Pick:
Option A.

Final Answer:
g depends on density times radius, so the ratio is 3 x 2.5 = 7.5. \[ \boxed{\text{(A) }7.5} \]