Motion In One Dimension Question 7

Question 7 - 30 January - Shift 2

An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth. Its velocity when it strikes the earth’s surface, ignoring air resistance, will be :

(1) $2 \sqrt{gR}$

(2) $\sqrt{g R}$

(3) $\sqrt{\frac{gR}{2}}$

(4) $\sqrt{2 gR}$

Show Answer

Answer: (2)

Solution:

Formula: Work-Energy Theorem

Loss in $PE=$ Gain in $KE$

$(-\frac{GMm}{2 R})-(-\frac{GMm}{R})=\frac{1}{2} mv^{2}$

$\Rightarrow v^{2}=\frac{GM}{R}=gR$

$\Rightarrow v=\sqrt{gR}$