First slide

Gravitaional potential energy

Question

When a projectile attains the escape velocity, then on surface of planet its

Moderate

A

KE is greater than PE numerically
B

PE is greater than KE numerically
C

Both PE and KE are numerically equal
D

None

Solution

If u = V_e
We can Write
$\large u=\sqrt{\frac{2GM}{R}}$
$\large \Rightarrow \frac{1}{2}mu^2=\frac{1}{2}m.X\frac{2GM}{R}\\\\ \Rightarrow \frac{1}{2}mu^2+(-\frac{GMm}{R})=0\\\\ \Rightarrow KE+PE=0\\\\ \Rightarrow |K.E|=|P.E|$

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