If V, R and g denote respectively the escape | vedclass

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Question

(D) To escape the surface of the earth,the kinetic energy of an object must be equal to the work done against gravity to move it from the surface to i

Vedclass · Accepted Answer

$V = \sqrt{2gR}$

Vedclass · Answer

(D) To escape the surface of the earth,the kinetic energy of an object must be equal to the work done against gravity to move it from the surface to infinity.The energy balance equation is given by: $\frac{1}{2}mv^2 = \frac{GMm}{R}$,where $M$ is the mass of the earth and $R$ is the radius of the earth.Solving for $v$,we get: $v = \sqrt{\frac{2GM}{R}}$.We know that the acceleration due to gravity at the surface is $g = \frac{GM}{R^2}$,which implies $GM = gR^2$.Substituting $GM = gR^2$ into the expression for $v$:$v = \sqrt{\frac{2(gR^2)}{R}} = \sqrt{2gR}$.Thus,the correct equation is $V = \sqrt{2gR}$.

If $V, R$ and $g$ denote respectively the escape velocity from the surface of the earth,the radius of the earth,and the acceleration due to gravity,then the correct equation is:

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