Q.1. Gravitational acceleration on the surface of a planet is √6/11 g. where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is 2/3 times that of the earth. If the escape speed on the surface of the earth is taken to be 11 kms^{–1}, the escape speed on the surface of the planet in kms^{–1} will be (2010)
Ans. 3
Solution.
Q.2. A bullet is fired vertically upwards with velocity v from the surface of a spherical planet. When it reaches its maximum height, its acceleration due to the planet's gravity is 1/4 th of its value of the surface of the planet. If the escape velocity from the planet is v_{esc} = v√N, then the value of N is (ignore energy loss due to atmosphere) (JEE Adv. 2015)
Ans. 2
Solution. Let h be the height to which the bullet rises
Now applying conservation of energy for the throw
Loss of kinetic energy = Gain in gravitaional potential energy
Comparing (i) & (ii) N = 2
Q.3. A large spherical mass M is fixed at one position and two identical point masses m are kept on a line passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of length ℓ and this assembly is free to move along the line connecting them. All three masses interact only through their mutual gravitational interaction.
When the point mass nearer to M is at a distance r = 3ℓ from M, the tension in the rod is zero for The valueof k is (JEE Adv. 2015)
Ans. 7
Solution. For the tension in the rod to be zero, the force on both the masses m and m should be equal in magnitude and direction. Therefore
327 docs185 tests

1. What is the formula for gravitational force between two objects? 
2. How does the gravitational force vary with distance? 
3. What is the difference between mass and weight? 
4. How does the gravitational force affect the motion of objects? 
5. What are some reallife applications of the concept of gravitation? 
327 docs185 tests


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