First slide

Motion of planets and satellites

Question

The escape velocity for a rat of mass 1 kg from the earth surface is $11.2 k m s^{- 1} .$ The escape velocity for an elephant of mass 6000 kg would be

Easy

A

$11.2 \times 10^{2} k m s^{- 1}$
B

$11.2 k m s^{- 1}$
C

$11.2 \times 10^{- 2} k m s^{- 1}$
D

none of these

Solution

Escape velocity is independent of mass of object. $V_{e} = \sqrt{\frac{2 G M}{R}} \Rightarrow V_{e} d e p e n d s o n m a s s o f p l a n e t, r a d i u s o f p l a n e t a n d h e i g h t o f o b j e c t f r o m t h e s u r f a c e o f t h e e a r t h \Rightarrow V_{e} d o e s n o t d e p e n d o n m a s s o f o b j e c t a n d a n g l e o f p r o j e c t i o n$

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