Gravitation 3 Question 5

8. A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth

(1998, 2M)

(a) the acceleration of S is always directed towards the centre of the earth

(b) the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant

(c) the total mechanical energy of S varies periodically with time

(d) the linear momentum of S remains constant in magnitude

Assertion and Reason

Mark your answer as

(a) If Statement I is true, Statement II is true; Statement II is the correct explanation for Statement I

(b) If Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I

(c) If Statement I is true; Statement II is false

(d) If Statement I is false; Statement II is true

Show Answer

Answer:

Correct Answer: 8. (a)

Solution:

  1. Force on satellite is always towards earth, therefore, acceleration of satellite S is always directed towards centre of the earth. Net torque of this gravitational force F about centre of earth is zero. Therefore, angular momentum (both in magnitude and direction ) of S about centre of earth is constant throughout. Since, the force F is conservative in nature, therefore mechanical energy of satellite remains constant. Speed of S is maximum when it is nearest to earth and minimum when it is farthest.


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