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:
- 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.
