A particle is projected vertically upwards from the surface of teh earth (radius $R_{e}$ ) with a kinetic energy equal to half of the minimum value needed for it to escape. The height to which it rises above the surface ot the earth is $\frac{R}{n}$ where $n$ is:

Question

A particle is projected vertically upwards from the surface of teh earth (radius

R_{e}

) with a kinetic energy equal to half of the minimum value needed for it to escape. The height to which it rises above the surface ot the earth is

\frac{R}{n}

where

n

is:

Toppr Admin · Accepted Answer

The correct option is A h-ReThe kinetic-energy needed to escape from the surface is given as-E-12mve2-12m-x221A-2GmRe-2-GMmRe-Since- the-potential energy at the maximum height will be equal to the sum of half kinetic-energy and the potential energy at the surface of the earth-It can be-written as-x2212-GMmRe-12GMmRe-x2212-GMmRe-h-12Re-1Re-h-h-Re-The maximum height is Re-

A particle is projected vertically upward from the surface of earth (radiusRe) with a kinetic energy equal to half of the minimum value needed for it to escape.The height to which it rises above the surface of earth ish=Reh=2Reh=Re/2h=3Re

A particle is projected vertically upward from the surface of earth (radius $R_{e}$ ) with a kinetic energy equal to half of the minimum value needed for it to escape.The height to which it rises above the surface of earth is
$h = R_{e}$
$h = 2 R_{e}$
$h = R_{e} / 2$
$h = 3 R_{e}$