Check the correctness of the physical relation:
`v= sqrt((2GM)/(R))` , where v is velocity, G is gavitational constant, M is mass and R is radius of the earth.

Check the correctness of the relation : v=sqrt((E )/(rho)) where the symbols have their usual meanings.

Prove that g = GM/R^2 , where M is mass and R is radius of earth.

Check the correctness of the relation T=2pisqrt((l)/(g)) , where T is the time period, l is the length of pendulum and g is acceleration due to gravity.

Check the correctness of relation F=(mv^(2))/(r ) using dimensional analysis.

An artificial satellite is revolving around a planet fo mass M and radius R, in a circular orbit of radius r. From Kepler's third law about te period fo a satellite around a common central bdy, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show usingn dimensional analysis, that T = k/R sqrt((r^3)/(g)) , where k is a dimensionless constant and g is acceleration due to gravity.

Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be 2MR^2//5 , where M is the mass of the sphere and R is the radius of the sphere.

State whether the equation y = y_0 sng (2pi)/v t is correct,where t is time and v is velocity.