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NTA Abhyas JEE Main2020PhysicsGravitationPractice

Two large spherical objects of mass M each (uniformly distributed) are fixed as shown in figure. A small point mass m is projected from point A heading towards center C 2 of second sphere. The minimum velocity of point mass so that it can reach upto second object at point B is n 3 G M 5 R . Then calculate n . [Neglect other gravitational forces]

Correct answer

08.00

Step-by-step solution

If the ball can reach the mid point of line connecting spheres, then it will get attracted towards B. (At midpoint gravitational intensity is zero) Using energy conservation, 1 2 m V 0 2 - G M m R - G M m 9 R = - 2 G M m 5 R + 0 Solving, V 0 = 8 3 G M 5 R ⇒ n = 8

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