A particle is projected from the mid-point of the line joining two fixed particles each of mass m. If the separation between the fixed particles is l , the minimum velocity of projection of the particle so as to escape is equal to

Question

A particle is projected from the mid-point of the line joining two fixed particles each of mass m. If the separation between the fixed particles is l , the minimum velocity of projection of the particle so as to escape is equal to, G m l, G m 2 l, 2 G m l, 2 2 G m l

MARKS App · Accepted Answer

The gravitational potential at the mid-point P = V = V 1 + V 2 = - G m l 2 - G m l 2 = - 4 G m l The gravitational potential energy U = - 4 G m m 0 l , m 0 = mass of particle When it is projected with a speed v, it just escapes to infinity, and the potential and kinetic energy will become zero. ⇒ ∆ K . E . + ∆ P . E . = 0 ⇒ 0 - 1 2 m 0 v 2 + 0 - - 4 G m m 0 l = 0 ⇒ v = 2 2 G m l

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