A planet of mass M and radius a is surrounding by an atmosphere of constant density consisting of a gas of molar mass mu . Find the temperature T of the atmosphere on the surface of the planet if the height of the atmosphere is h lt lt a.

The density of asir ner earth's surface is 1.3kgm^-3 and the atmospheric pressure is 1.0xx10^5Nm^-2 . If the atmosphere had uniform density, same as that observed at the surface of the earth what would be the height of the atmosphere to exert the same pressure?

What would be the height of the atmosphere if the air density (a) were uniform and (b) decreased linearly to zero with height? Assume that at sea level the air pressure is 1.0 atm and the air density is 1.3 kg/ m^(3)

Diameter of a planet is 10d_(@) , its mean density is (rho_(@))/(4) and mass of its atmosphere is 10m_(@) where d^(@) , rho^(@) and m^(@) are diameter, mean density and mass of atmosphere respectively for the earth. Assume that mean density of atmosphere is same on the planet and the earth and height of atmosphere on both the planets is very small compared to their radius. Find the ratio of atmospheric pressure on the surface of the planet to that on the earth. If a mercury barometer reads 76 cm on the surface of the earth, find its reading on the surface of the planet.

Water and gasoline surface of relative density 1 and 0.6 are open to the atmosphere at the same elevation. Find the height h of the third liquid of relative density 1.6 in the right leg as shown in

Find the height of a cone of radius 5 cm and slant height 13 cm.

Find the height of image in the following diagram.

Find the height of an equilateral triangle having side 2a