Work done in taking a body of mass m to a height nR above surface of earth will be: ( R = radius of earth )

Question

Work done in taking a body of mass m to a height nR above surface of earth will be: ( R = radius of earth ) (A) mgn R (B) m g R (n/(n+1)) (C) m g R ((n+1)/n) (D) ( mgR / n ( n +1))

Tardigrade Admin · Accepted Answer

W =( GmM / R )-( GmM / nR + R ) =( GMm / R )[1-(1/ n )]=( GMm / R )[( n / n +1)] = mgR (( n / n +1))

Q. Work done in taking a body of mass $m$ to a height $n R$ above surface of earth will be : $(R =$ radius of earth $)$

$m g n R$

$m g R \frac{n}{( n + 1 )}$

$m g R \frac{( n + 1 )}{n}$

$\frac{m g R}{n ( n + 1 )}$

$W = \frac{G m M}{R} - \frac{G m M}{n R + R}$
$= \frac{GM m}{R} [1 - \frac{1}{n}] = \frac{GM m}{R} [\frac{n}{n + 1}]$
$= m g R (\frac{n}{n + 1})$

Q. Work done in taking a body of mass m to a height nR above surface of earth will be : (R= radius of earth )

mgnR

mgR(n+1)n​

mgRn(n+1)​

n(n+1)mgR​