First slide

Gravitaional potential energy

Question

The magnitude of gravitational potential energy of the moon-earth system is U with zero potential energy at infinite separation. The kinetic energy of the moon with respect to the earth is K.

Easy

A

U < K
B

U > K
C

U = K
D

None

Solution

Potential energy of earth-moon system = $\large -\frac {GM_eM_m}{r}$
$\large \therefore U=\frac{GM_eM_m}{r}$
Moon's orbit is circular .So orbital speed of moon
$\large V=\sqrt{\frac{GM}{r}}$
K.E. of moon = K = $\large =\frac12mV^2=\frac{GMm}{2r}$

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