The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is $2\,s$. The period of oscillation of the same pendulum on the planet would be

A weight is suspended from the ceiling of a lift by a spring balance. When the lift is stationary the spring balance reads $W$. If the lift suddenly falls freely under gravity, the reading on the spring balance will be

The radius of earth is about $6400\; km$ and that of mars is $3200\; km$. The mass of the earth is about $10$ times mass of mars. An object weighs $200 \;N$ on the surface of earth. Its weight on the surface of mars will be .......... $N$

The gravitational potential at a point above the surface of earth is $-5.12 \times 10^7 \mathrm{~J} / \mathrm{kg}$ and the acceleration due to gravity at that point is $6.4 \mathrm{~m} / \mathrm{s}^2$. Assume that the mean radius of earth to be $6400 \mathrm{~km}$. The height of this point above the earth's surface is :

A particle of mass $10\, g$ is kept of the surface of a uniform sphere of mass $100\, kg$ and a radius of $10\, cm .$ Find the work to be done against the gravitational force between them to take the particle far away from the sphere. (you make take $\left.G=6.67 \times 10^{-11} Nm ^{2} / kg ^{2}\right)$

If the angular speed of the earth is doubled, the value of acceleration due to gravity (g) at the north pole