Question:
Assuming the mass of Earth to be ten times the mass of Mars and its radius to be twice the radius of Mars and the acceleration due to gravity on the surface of Earth to be $10$ m/s$^2$, the acceleration due to gravity on the surface of Mars is
Assuming the mass of Earth to be ten times the mass of Mars and its radius to be twice the radius of Mars and the acceleration due to gravity on the surface of Earth to be $10$ m/s$^2$, the acceleration due to gravity on the surface of Mars is
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Always use ratio form in gravity problems to simplify calculations.
Updated On: May 1, 2026
- $0.2$ m/s$^2$
- $0.4$ m/s$^2$
- $2$ m/s$^2$
- $4$ m/s$^2$
- $5$ m/s$^2$
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The Correct Option is D
Solution and Explanation
Concept:
\[ g = \frac{GM}{R^2} \]
Step 1: Take ratio.
\[ \frac{g_E}{g_M} = \frac{M_E}{M_M} \cdot \frac{R_M^2}{R_E^2} \]
Step 2: Substitute given values.
\[ \frac{g_E}{g_M} = \frac{10}{1} \cdot \frac{1}{(2)^2} = \frac{10}{4} = 2.5 \]
Step 3: Solve.
\[ \frac{10}{g_M} = 2.5 \Rightarrow g_M = 4 \]
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