Question

The acceleration due to gravity on the surface of the moon is (1)/(6) that on earth and the diameter of the moon is one-fourth that of earth. The ratio of escape velocities on earth and moon will be:

• A. \( \dfrac{\sqrt{6}}{2} \)
• B. \( \sqrt{24} \)
• C. 3
• D. dfrac√(3)2

Hint:

Escape velocity depends on both surface gravity and radius of the planet.

Answer 1

The Correct Option is A

Step 1: Escape velocity: vₑ = √(2gR)
Step 2: Ratio: (vₑ)/(vm) = √((gₑ Rₑ)/(gm Rm))
Step 3: Substitute: (vₑ)/(vm) = √((gₑ Rₑ)/((gₑ)/(6)· (Rₑ)/(4))) = √(24) = dfrac√(6)2