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 2s. The period of oscillation of the same pendulum on the planet would be:

Choose the correct statement (G is universal gravitational constant.)

The mass density of a planet of radius R varies with the distance r from its centre as ρ(r) = ρ₀ $(1-\frac{{\mathrm{r}}^2}{{\mathrm{R}}^2}).$ Then the gravitational field is maximum at:

The acceleration due to gravity on the earth's surface at the poles is g and angular velocity of the earth about the axis passing through the pole is ω. An object is weighed at the equator and at a height h above the poles by using a spring balance. If the weights are found to be same, then h is : (h << R, where R is the radius of the earth)

A homogeneous disc with a radius 0.2 m and mass 5 kg rotates about an axis passing through its centre and perpendicular to its plane. The angular velocity of the rotating  disc as a function of time is given by the formula ω = 2 + 6t, where ω is in rad/sec.  The tangential force ( in newton) applied to the rim of the disc is :