Integer Answer Type Questions: Gravitation | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE PDF Download

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