A rocket of mass M is launched vertically from the surface of the earth with an

Question

A rocket of mass M is launched vertically from the surface of the earth with an initial speed V. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is

Options:

A . R(gR2V2−1)

B . R(gR2V2−1)

C . R(2gRV2−1)

D . R(2gRV2−1)

Answer: Option C
:
C

Δ K . E = Δ U \Rightarrow \frac{1}{2} M V^{2} = G M_{e} M (\frac{1}{R} - \frac{1}{R + h}) \dots \dots (i) A l s o g = \frac{G M_{e}}{R^{2}} \dots \dots (i i) O n s o l v i n g (i) a n d (i i) h = \frac{R}{(\frac{2 g R}{V^{2}} - 1)}

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