The escape velocity of a body on a planet ‘A’ is 12 kms–1. The escape velocity of the body on another planet ‘B’, whose density is four times and radius is half of the planet ‘A’, is
- 12 kms–1
- 24 kms–1
- 36 kms–1
- 6 kms–1
The Correct Option is A
Solution and Explanation
Th correct option is(A): 12 kms–1
\(v_{esc}=\sqrt\frac{2GM}{R}=\sqrt\frac{2G}{R}×p×\frac{4}{3}{\pi}R^3\)
\(⇒v_{esc}∝R\sqrt{p}\)
\(⇒\frac{(v_esc)B}{(vesc)A}=1\)
⇒ (vesc)B = 12 km/s
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Concepts Used:
Speed and Velocity
The rate at which an object covers a certain distance is commonly known as speed.
The rate at which an object changes position in a certain direction is called velocity.
Difference Between Speed and Velocity:
Read More: Difference Between Speed and Velocity