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NTA Abhyas JEE Main2020PhysicsGravitationPractice

A large sphere of mass M is fixed at one position and two identical particles each of mass m are kept on a line passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of length l and this assembly is free to move along the line connecting them. All three masses interact only through their mutual gravitational interaction. When the point mass nearer to M is at a distance r

Correct answer

7

Step-by-step solution

Due to gravitational interaction connected masses have some acceleration. Let both small masses are moving with acceleration 'a' towards larger mass M Force equation for mass nearer to a larger mass G M m 3 l 2 - G m 2 l 2 = m a ...(i) Force equation for mass away from a larger mass G M m 4 l 2 + G m 2 l 2 = m a ...(ii) From equation (i) & (ii) G M 9 l 2 - G m l 2 = G M 16 l 2 + G m l 2 ⇒ M 9 - M 16 = m + m 7 M 144 = 2 m ⇒ m = 7 M 288 = k M 288 ⇒ k = 7

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