Question

# A body is projected vertically upwards from the bottom of a crater of moon of depth R100 where R is the radius of moon with a velocity equal to the escape velocity on the surface of moon. Maximum height attained by the body from the surface of the moon is KR.The value of K is

Open in App
Solution

## BC is the crater of moon. B denotes bottom of crater. Depth of crater = R100 Radius of moon = R Speed of particle at B=VB Escape velocity on surface of moon =Ve ∴Ve=√2GMR At highest point VA=0 Mechanical energy is conserved in the process Decrease in kinetic energy =12mV2B Increase in PE=UA−UB VA=Potential at A=−GM(R+h) h = height from surface Potential at B= VB=−GMR3[32R2−12r2] =−GMR3[1.5R2−0.5(R−R100)2] =−GMR(1.01) ∴ Increase in PE =−GMmR+h+GMmR×(1.01) Decrease in KE = increase in PE 12mV2B=−GMm(R+h)+GMm×1.01R GMR=GM[−1R+h+1.01R] or 1R=−1R+h+1.01R or h=99R

Suggest Corrections
10
Join BYJU'S Learning Program
Related Videos
Relative Motion
PHYSICS
Watch in App
Explore more
Join BYJU'S Learning Program