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Q.

What is the minimum energy required to launch a satellite of mass m from the surface of earth of mass M, radius R in a circular orbit at an altitude 2R

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a

5GmM6R

b

5GMmR

c

−GMm6R

d

−GMm3R

answer is A.

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Detailed Solution

The minimum energy required to launch a satellite at height h = 2R

When it is on surface T.E1=P.E=−GMmR

When it is launched at a height = h = 2R

T.E2=−GMm2(R+h)=−GMm6R

ΔT.E=T.E2−T.E1=−GMm6R+GMmR=5GMm6R

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What is the minimum energy required to launch a satellite of mass m from the surface of earth of mass M, radius R in a circular orbit at an altitude 2R