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
(a) Vₑ = 2V (b) Vₑ = V
(c) Vₑ = V/2 (d) Vₑ = √3V

Answer 1

Answer:

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Explanation:

The g at poles is given by g

p

=

R

2

GM

Now, g at equator, g

e

=

2

g

p

=

2R

2

GM

But, acceleration on body at equator =g

p

−

R

V

2

⇒

R

2

GM

−

R

V

2

=

2R

2

GM

solving, we get V=(

2R

2

GM

)

0.5

Now, escape velocity at poles, V

e

=(

R

2

2GM

)

0.5

=(4×

R

2

GM

)

0.5

=2V.