If the Earth is assumed to be a sphere of uniform mass density and its weight on the surface is 200 N , then the weight of the body at a depth halfway to the Earth's center will be

If gravitational attraction between two points masses be given by $F=G \frac{m_1 m_2}{r^n}$, then the period of a satellite in a circular orbit will be proportional to

The distance of the centres of Moon and the Earth is $D$. The mass of the Earth is 81 times the mass of the Moon. At what distance from the centre of the Earth, the gravitational force on a particle will be zero?

The gravitational field in a region is given by $$\mathbf{E}=5 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{i}}+12 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{j}}$$. The change in the gravitational potential energy of a particle of mass $$1 \mathrm{~kg}$$ when it is taken from the origin to a point ($$5 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}$$) is