Question 126: Gravitation

Question

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

Accepted Answer

$${U_P} =  - {{GMm} \over {2R}}$$
$${U_S} =  - {{GMm} \over R}$$
$$\Rightarrow$$ Energy conservation
$${1 \over 2}m{v^2} - {{GMm} \over R} =  - {{GMm} \over {2R}}$$
$${v^2} = {{GM} \over R}$$
$$v = \sqrt {{{GM} \over R}}  = \sqrt {gR} $$

Answer

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

Answer

$\sqrt{g R}$

Answer

$\sqrt{2 g R}$

Answer

$2 \sqrt{g R}$

Gravitation

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

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