A satellite is moving with a constant speed v in a circular orbit… - Vidyadip

MCQ

A satellite is moving with a constant speed v in a circular orbit about the earth. An object of mass m is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is:

A
$\frac{1}{3} m v^2$
B
$mv ^2$
C
$\frac{1}{2} m v^2$
D
$\frac{2}{3} m v^2$

✓

Answer

(b) $mv ^2$
Explanation: Escape speed $=\sqrt{2} \times$ orbital speed
$
v_e=\sqrt{2} v
$
At the time of its ejection, kinetic energy of the object will be
$
K=\frac{1}{2} m v_e^2=\frac{1}{2} m(\sqrt{2} v)^2=mv^2
$

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