Consider a spherical planet rotating about its axis. The velocity of a point at equator is v. The angular velocity of this planet is such that it makes apparent value of ‘g’ at the equator half of value of ‘g’ at the pole. The escape speed for a polar particle on the planet expressed as multiple of v is :

Options

A. v
B. 2v
C. 3v
D. 4v

Explanation

According to question (At equator)
`Mg-(Mv^(2))/(R)=(Mg)/(2)impliesv^(2)=(Rg)/(2)=(GM)/(2R)`
using conservation of energy `-(GMm)/(R)+(1)/(2)mv_(e)^(2)=0impliesv_(e)^(2)=(2GM)/(R)=4v^(2)`