Consider the following statements: The gravitational force exerted by the sun on the moon is greater than the gravitational force exerted by the earth on the moon. A heavy body falls at a faster rate than a light body in vacuum. Which of the following statements given above is/are correct ?
Consider the following statements: The gravitational force exerted by the sun on the moon is greater than the gravitational force exerted by the earth on the moon. A heavy body falls at a faster rate than a light body in vacuum. Which of the following statements given above is/are correct ? Correct Answer 1 only
The gravitational force F between two bodies is directly proportional to the product of masses of those bodies. Here, since the product m1 and m2 are greater for the sun and the moon than that of the earth and the moon (because the mass of the sun is greater than that of the earth), therefore F exerted by the sun on the moon is greater than the F exerted by the earth on the moon.
F between sun and moon:
G m1m2/r2 = G*6.49*1036 N
F between earth and moon
G m1m2/r2 = G*2.975*1036 N
This shows that the gravitational force between the sun and moon is greater. but almost equal to that of earth . That's why it stays in orbit.
- As the mass of the sun is much more than the mass of the earth, so the sun will apply more gravitational force on moon compared to earth. So statement 1 is correct.
- Since acceleration due to gravity for both heavy and the light object will be same. So they will have same acceleration in vacuum and travel together. So statement 2 is wrong.