with what velocity should a body be thrown up so that it rise to a height equal to the radius - Physics -

Question

with what velocity should a body be thrown up so that it rise to
a height equal to the radius of the earth(g=10ms-
2at the surface)?

Komal Jain · Accepted Answer

When the body is thrown , the work is done against the
gravitational attraction
Small work done in taking the body by a distance dx,
dW=Fdx=GMmx2dxTherefore, the work done in taking the body to a
height equal to the radius of the
earth,W=∫R2RGMmx2dx⇒W=GMm∫R2Rx-2dx⇒W=GMmx-2+1-2+1R2R⇒W=-GMm1xR2R=-GMm12R-1R=-GMmR-2R2R2⇒W=GMm2RThis
work is done at the cost of the kinetic energy given to the body,K
E=GMm2R⇒12mv2=GMm2R⇒v=GMR=GMR2×R=gR=10×6
4×106=8×103 m/s

with what velocity should a body be thrown up so that it rise to a height equal to the radius of the earth(g=10ms- 2at the surface)?

with what velocity should a body be thrown up so that it rise to a height equal to the radius of the earth(g=10ms^- ²at the surface)?