First slide

Gravitaional potential energy

Question

If g is the acceleration due to gravity on the earth’s surface, the change in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is

Easy

A

mgR/2
B

2mgR
C

mgR
D

-mgR

Solution

$\begin{array}{l} u_{g} = - \frac{{GM}_{1} M_{2}}{R} \\ \Rightarrow u_{f} - u_{i} = - \frac{GMm}{2 R} - \frac{GMm}{R} \\ Δu = \frac{GMm}{2 R} = \frac{mgR}{2} \{g = \frac{GM}{R^{2}}\} \end{array}$

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