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7.Gravitation
hard
A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is $V.$ Due to the rotation of planet about its axis the acceleration due to gravity $g$ at equator is $1/2$ of $g$ at poles. The escape velocity of a particle on the planet in terms of $V.$
A
$V_e = 2V$
B
$V_e = V$
C
$V_e = V /2$
D
$V_e =\sqrt{3} V$
Solution
$g_{e}=g_{p}-R \omega^{2} \Rightarrow \frac{g}{2}=g-R \omega^{2}$
$R \omega^{2}=\frac{g}{2} \Rightarrow R^{2} \omega^{2}=\frac{g R}{2}$
$V^{2}=\frac{g R}{2} \ldots \ldots(1)$
$V_{e}=\sqrt{2 g R} \ldots \ldots(2)$
From $(1)$ and $(2)$
$V_{e}=\sqrt{2 \times 2 V^{2}} \Rightarrow V_{e}=2 V$
Standard 11
Physics
