A body of mass m rises to height h=R / 5 from the earth's surface, where R is earth's radius. If g is acceleration due to gravity at earth's surface, the increase in potential energy is

Question

A body of mass m rises to height h=R / 5 from the earth's surface, where R is earth's radius. If g is acceleration due to gravity at earth's surface, the increase in potential energy is (A) mg / h (B) (5/6) mgh (C) (3/5) mgh (D) (6/7) mgh

Tardigrade Admin · Accepted Answer

U f = u i =(- GmM /( R +( R )5))+( GmM / R ) =(-5 GmM /6 R )+( GmM / R ) =( GmM /6 R )=( mgR /6)

Q. A body of mass $m$ rises to height $h = R /5$ from the earth's surface, where $R$ is earth's radius. If $g$ is acceleration due to gravity at earth's surface, the increase in potential energy is

$m g / h$

$\frac{5}{6} m g h$

$\frac{3}{5} m g h$

$\frac{6}{7} m g h$

$U_{f} = u_{i} = \frac{- G m M}{( R + \frac{R}{5} )} + \frac{G m M}{R}$
$= \frac{- 5 G m M}{6 R} + \frac{G m M}{R}$
$= \frac{G m M}{6 R} = \frac{m g R}{6}$

Q. A body of mass m rises to height h=R/5 from the earth's surface, where R is earth's radius. If g is acceleration due to gravity at earth's surface, the increase in potential energy is

mg/h

65​mgh

53​mgh

76​mgh