The ratio of gravitational acceleration at he | vedclass

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(B) The gravitational acceleration $g_h$ at a height $h$ from the surface of the earth is given by the formula:$g_h = g \left( \frac{R}{R+h} \right)^2

Vedclass · Accepted Answer

$25/16$

Vedclass · Answer

(B) The gravitational acceleration $g_h$ at a height $h$ from the surface of the earth is given by the formula:$g_h = g \left( \frac{R}{R+h} \right)^2$where $g$ is the acceleration due to gravity at the surface of the earth.For height $h_1 = 3R$,the acceleration is:$g_1 = g \left( \frac{R}{R+3R} \right)^2 = g \left( \frac{R}{4R} \right)^2 = g \left( \frac{1}{4} \right)^2 = \frac{g}{16}$For height $h_2 = 4R$,the acceleration is:$g_2 = g \left( \frac{R}{R+4R} \right)^2 = g \left( \frac{R}{5R} \right)^2 = g \left( \frac{1}{5} \right)^2 = \frac{g}{25}$The ratio of gravitational acceleration at height $3R$ to that at height $4R$ is:$\frac{g_1}{g_2} = \frac{g/16}{g/25} = \frac{25}{16}$Thus,the correct option is $B$.

The ratio of gravitational acceleration at height $3R$ to that at height $4R$ from the surface of the earth is (where $R$ is the radius of the earth):

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