Question

The work done to raise a mass m from the surfac
of the earth to a height h, which is equal to th
radius of the earth, is
[NEET-2019]
(1) mgR.
(2) 2mgR
(3)1/2mgR
(4)3/2mgR​

Answer 1

AnswEr :

To find the work done in lifting an object of mass 'm' to a height 'h' which is equal to Earth' radius.

Initial Potential Energy in the object would be :

$\sf U_o = - \dfrac{GMm}{R}$

When the object is lifted to a height 'h' :

$\sf U= - \dfrac{GMm}{R + h}$

Here, h = radius of earth.

$\longrightarrow \: \sf U = - \dfrac{GMm}{2R}$

Now,

$\implies\sf W= U - U_o \\ \\ \implies \sf \: W = \dfrac{GMm}{R} \big(1 - \dfrac{1}{2} ) \\ \\ \implies \sf \: W = \dfrac{GMm}{r}$

Also,

$\sf \: mg = \dfrac{GMm}{R {}^{2} } \\ \\ \longrightarrow \sf \: g {R}^{2} = GM$

Thus,

$\implies \sf \: W = \dfrac{ {mgR}^{2} }{2R} \\ \\ \implies \boxed{ \boxed{ \sf W = \dfrac{mgR}{2} }}$

Option (C) is correct