If $R$ is radius of the earth and $W$ is work done in lifting a body from the ground to an altitude $R$ , the work which should be done in lifting it further to twice that altitude is:

\frac{W}{2}

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W

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\frac{W}{3}

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3 W

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Solution

The correct option is A $\frac{W}{2}$
Work done is equal to change in PE.

$W = - Δ U = U_{1} - U_{2} = - \frac{G M m}{R} - (- \frac{G M m}{2 R}) = - \frac{G M m}{2 R}$

Work done in lifting body from $2 R$ to $4 R$ .

$W^{'} = - Δ U = U_{1} - U_{2} = - \frac{G M m}{2 R} - (- \frac{G M m}{4 R}) = - \frac{G M m}{4 R} = \frac{W}{2}$

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If R is radius of the earth and W is work done in lifting a body from the ground to an altitude R, the work which should be done in lifting it further to twice that altitude is:

The correct option is A W2Work done is equal to change in PE.W=−ΔU=U1−U2=−GMmR−(−GMm2R)=−GMm2RWork done in lifting body from 2R to 4R.W′=−ΔU=U1−U2=−GMm2R−(−GMm4R)=−GMm4R=W2

If $R$ is radius of the earth and $W$ is work done in lifting a body from the ground to an altitude $R$ , the work which should be done in lifting it further to twice that altitude is: