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A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R ( R = radius of the earth), it ejects a rocket of mass m 10 so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is ( G is the gravitational constant; M is the mass of the earth):

Options

  1. Am 20 u 2 + 113 200 G M R
  2. B5 m u 2 - 119 200 G M R
  3. C3 m 8 u + 5 G M 6 R 2
  4. Dm 20 u - 2 G M 3 R 2

Correct answer

B. 5 m u 2 - 119 200 G M R

Step-by-step solution

- G M e m R + 1 2 m u 2 = - G M e m 2 R + 1 2 m v 2 v = u 2 - G M e R M 10 v r = M u 2 - G M e R Kinetic energy = 1 2 M 10 V T 2 + V r 2 = M 20 81 GM 2 R + 100 u 2 - 100 GM R = M 20 100 u 2 − 119 G M 2 R = 5 m u 2 - 119 GM 200 R

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