Assuming the orbit of mars around the sun to be circular, the revolving red planet's angular momentum is proportional to the nth power of its radius. Here n is

Options

A. 1
B. 2
C. `1/2`
D. 1.5

Answer

C

Explanation

The C.P. force `(mv^2)/R` is provided by the gravitational force `(GMm)/(R^2)`
`therefore (mv^2)/R = (GMm)/(R^2) therefore v = sqrt((GM)/R)`
But the angular momentum
`L = Iomega = mR^2 xx v/R = mvR `
`therefore L = mR sqrt((GM)/(R)) = msqrt(GM) xx R/(sqrtR)`
`= msqrt(GM). R^(1/2) = KR^(1/2)`
`therefore L prop R^(1/2)` as `K = msqrt(GM)` is a constant.
But `L prop R^n therefore n = 1/2`