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Show that if a body be projected vertica...

Show that if a body be projected vertically upward from the surface of the earth so as to reach a height `nR` above the surface
(i) the increase in its potential energy is `((n)/(n + 1)) mgR`,
(ii) the velocity with it must be projected is `sqrt((2ngR)/(n + 1))`, where `r` is the radius of the earth and `m` the mass of body.

Text Solution

Verified by Experts

The correct Answer is:
A
(i) `Delta U = (mgh)/(1 + (h)/(R))`
putting `h = nR`, we get
`Delta U = ((n)/(n + 1))mgR`
(ii) `Delta U = ((n)/(n + 1))mgR`
`(1)/(2) m nu^(2)`
`:. nu = sqrt((2ngR)/(n + 1))`
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