First slide

Gravitational potential and potential energy

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

Moderate

A

$m g h$
B

$\frac{4}{5} m g h$
C

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

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

Solution

$Δ U = \frac{m g h}{1 + h / R} S u b s t i t u t i n g R = 5 h w e g e t Δ U = \frac{m g h}{1 + 1 / 5} = \frac{m g h}{\frac{5 + 1}{5}} = \frac{5}{6} m g h$

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