SATHEE: Gravitation Question 356

Gravitation Question 356

Question: 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 pole of planet in terms of v is

Options:

A) $[v_{e} = 2 v]$

B) $[v_{e} = v]$

C) $[v_{e} = v / 2]$

D) $[v_{e} = \sqrt{3} v]$

Show Answer

Answer:

Correct Answer: A

Solution:

$[v = ω R]$

$[g = g_{0} - ω^{2} R]$ [ $[g =]$

at equator, $[g_{0} =]$ at poles] $[\frac{g_{0}}{2} = g_{0} - ω^{2} R; ω^{2} R = \frac{g_{0}}{2}]$

$[v^{2} = \frac{g_{0} R}{2}]$

$[v_{e} = \sqrt{2 g_{0} R} = \sqrt{4 v^{2}} = 2 v]$

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Gravitation Question 356

Question: 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 pole of planet in terms of v is

Options:

Answer:

Solution:

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