An object is allowed to fall from a height R above the Earth, where R is the radius of the Earth. Its velocity when it strikes the Earth's surface, ignoring air resistance, will be [2023]

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Solution

Q.
An object is allowed to fall from a height R above the Earth, where R is the radius of the Earth. Its velocity when it strikes the Earth's surface, ignoring air resistance, will be [2023]

1 $2 \sqrt{g R}$

2 $\sqrt{g R}$

3 $\sqrt{\frac{g R}{2}}$

4 $\sqrt{2 g R}$

Ans.
(2)

$Loss in PE = Gain in KE$

$(- \frac{G M m}{2 R}) - (- \frac{G M m}{R}) = \frac{1}{2} m v^{2}$

$\Rightarrow v^{2} = \frac{G M}{R} = g R$

$\Rightarrow v = \sqrt{g R}$

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