A satellite of mass m revolves around the ear | vedclass

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Question

(D) The gravitational force acting on the satellite provides the necessary centripetal force for its circular orbit.Let $M_e$ be the mass of the earth

Vedclass · Accepted Answer

$\left( \frac{gR^2}{R + x} \right)^{1/2}$

Vedclass · Answer

(D) The gravitational force acting on the satellite provides the necessary centripetal force for its circular orbit.Let $M_e$ be the mass of the earth. The gravitational force is $F_g = \frac{G M_e m}{(R + x)^2}$.The centripetal force required is $F_c = \frac{m v_0^2}{R + x}$.Equating these,we get $\frac{G M_e m}{(R + x)^2} = \frac{m v_0^2}{R + x}$,which simplifies to $v_0^2 = \frac{G M_e}{R + x}$.We know that the acceleration due to gravity on the earth's surface is $g = \frac{G M_e}{R^2}$,which implies $G M_e = g R^2$.Substituting this into the expression for $v_0^2$,we get $v_0^2 = \frac{g R^2}{R + x}$.Therefore,the orbital speed is $v_0 = \sqrt{\frac{g R^2}{R + x}} = \left( \frac{g R^2}{R + x} \right)^{1/2}$.

$A$ satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the earth,the orbital speed of the satellite is

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