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IAT IISER2023PhysicsGravitation

Two spherical bodies A and B each of mass M and radius R are located such that their centers are apart by a distance of 4 R as shown in the figure. An object C of mass m is thrown from the surface of A directly towards the center of B with a speed v₀=2 v_ , where v_ is the minimum speed needed for C to reach the surface of B . Given that G is the universal gravitational constant, how does the speed v(x) of C change a

Options

  1. Av(x)= G M R x^ 1 / 2 (4 R-x)^ 1 / 2
  2. Bv(x)= 2 R 2 G M R x(4 R-x)
  3. Cv(x)= 6 R^2 2 G M R x^ 3 / 2 (4 R-x)^ 3 / 2
  4. Dv(x)= 2 2 G M R x^ 1 / 2 (4 R-x)^ 1 / 2

Correct answer

D. v(x)= 2 2 G M R x^ 1 / 2 (4 R-x)^ 1 / 2

Step-by-step solution

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