The mass density of a planet of radius R varie with the distance r form its centre as `rho (r) = p_(0) ( 1 - (r^(2))/(R^(2))) `. Then the graviational field is maximum at :

A cylindrical wire of radius R has current density varying with distance r form its axis as J(x)=J_0(1-(r^2)/(R^2)) . The total current through the wire is

Mass density of sphere having radius R varies as rho = rho_0(1-r^2/R^2) . Find maxium magnitude of gravitational field

The distance of the centre of mass of a hemispherical shell of radius R from its centre is

The earth is a homogeneous sphere of mass M and radius R. There is another spherical planet of mass M and radius R whose density changes with distance r from the centre as p=p_(0)r. (a) Find the ratio of acceleration due to gravity on the surface of the earth and that on the surface of the planet. (b) Find p_(0).

Charge density of a sphere of radius R is rho = rho_0/r where r is distance from centre of sphere.Total charge of sphere will be

If the radius of a planet is R and its density is rho , the escape velocity from its surface will be

The mass density of a spherical galaxy varies as (K)/(r) over a large distance 'r' from its centre . In that region , a small star is in a circular orbit of radius R . Then the period of revolution , T depends on R as :

Consider a spherical planet of radius R . Its density varies with the distance of its centre t as rho=A-Br , where A and B are positive constants. Now answer the following questions. Acceleration due to gravity at a distance r(rltR) from its centre is