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-dfrac-W-2-dfrac-W-3-W3W

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Toppr Admin · Accepted Answer

Work done is equal to change in PE-W-x2212-x394-U-U1-x2212-U2-x2212-GMmR-x2212-x2212-GMm2R-x2212-GMm2RWork done in lifting body from 2R to 4R-W-x2032-x2212-x394-U-U1-x2212-U2-x2212-GMm2R-x2212-x2212-GMm4R-x2212-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:
$\frac{W}{2}$
$\frac{W}{3}$
$W$
$3 W$

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 $4 R$ .

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

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:W2W3W3W

Work 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:
$\frac{W}{2}$
$\frac{W}{3}$
$W$
$3 W$

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 $4 R$ .

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