The mass of earth is increasing at the rate of 1 part in `5 xx 10^(19)` per day due to the acceleration of meteors falling normally on the surface of earth evenly everywhere. Find the corresponding change of period of rotation of earth , taking the earth to be a sphere of uniform density :

The mass of the earth is increasing at the rate 1 part in 5 xx 20^(19) per day by the accretion of meteors falling normally upon the earth's surface. Find the corresponding rate of change of the period of rotation of the earth supporting the earth to be a sphere of uniform density. [Hint: Consider the deposit as a spherical shell and apply principle of conservation of angular momentum]

The mass of the Earth is 6 xx 10^(24) kg and its radius is 6400 km. Find the acceleration due to gravity on the surface of the Earth.

Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density).

Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density).

The moon's radius is 1//4 that of the earth and its mass 1//80 times that of the earth. If generates the acceleration due to gravity on the surface of the earth, that on the surface of the moon is