Gravitation - Mechanics Physics PYQs

The distance through which one has to dig the Earth from its surface, so as to reach the point where the acceleration due to gravity is reduced by 40% of that at the surface of the Earth, is (radius of Earth is 6400 km)

Infinite number of masses each of 3kg are placed along a straight line at the distances of 1 m, 2m, 4m, 8m, ...... from a point O on the same line. If G is the universal gravitational constant, then the magnitude of gravitational field intensity at O is

A particle is kept on the surface of a uniform sphere of mass 1000 kg and radius 1 m. The work done per unit mass against the gravitational force between them is

[G = 6.67 \(\times\) 10\(^{-11}\) Nm\(^2\) kg\(^{-2}\)]

If the Earth stops rotating in its orbit about the sun, there will be variation in the weight of our bodies at

At what depth below surface of the Earth, the acceleration due to gravity will be half of its value that at \(1600 \mathrm{~km}\) above the surface of the Earth?

The gravitational potential energy is maximum at

A geostationary satellite is taken to a new orbit, such that its distance from centre of the earth is doubled. Then, find the time period of this satellite in the new orbit.

A uniform solid sphere of radius \(R\) produces a gravitational acceleration of \(a_0\) on its surface. The distance of the point from the centre of the sphere where the gravitational acceleration becomes \(\frac{a_0}{4}\) is

A projectile is thrown straight upward from the earth's surface with an initial speed \(v=\alpha v_e\) where \(\alpha\) is a constant and \(v_e\) is the escape speed. The projectile travels upto a height 800 km from earth's surface, before it comes to rest. The value of the constant \(\alpha\) is (radius of the earth \(=6400 \mathrm{~km}\))

Statement (A) Two artificial satellites revolving in the same circular orbit have same period of revolution.

Statement (B) The orbital velocity is inversely proportional to the square root of radius of the orbit.

Statement (C) The escape velocity of the body is independent of the altitude of the point of projection.