A mass m is raised from a distance 2R from the surface of the earth to 3R . Work done to do so against gravity will -

Question

A mass m is raised from a distance 2R from the surface of the earth to 3R . Work done to do so against gravity will - (A) (m g R/10) (B) (m g R/11) (C) (m g R/12) (D) (m g R/14)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-hr5hvozo3svs7qut.jpg" /> Ui=- (G M m/(2 R + R)) Uf=- (G M m/(R + 3 R)) W=Δ U=Uf- Uf =(G M m/12 R)=(G M/R2) × (m R/12) =mgR/12

Q. A mass $m$ is raised from a distance $2 R$ from the surface of the earth to $3 R$ . Work done to do so against gravity will -

$\frac{m g R}{10}$

$\frac{m g R}{11}$

$\frac{m g R}{12}$

$\frac{m g R}{14}$

$U_{i} = - \frac{GM m}{( 2 R + R )}$
$U_{f} = - \frac{GM m}{( R + 3 R )}$
$W = Δ U = U_{f} - U_{f}$
$= \frac{GM m}{12 R} = \frac{GM}{R ^{2}} \times \frac{m R}{12}$
$= m g R /12$

Q. A mass m is raised from a distance 2R from the surface of the earth to 3R . Work done to do so against gravity will -

10mgR​

11mgR​

12mgR​

14mgR​