A rope of length `30cm` is on a horizontal table with maximum length hanging from edge `A` of the table. The coefficient of friction between the rope and table is `0.5`. The distance of centre of mass of the rope from `A` is

Options

A. `(5sqrt(15))/3 cm`
B. `(5sqrt(17))/3 cm`
C. `(5sqrt(19))/3 cm`
D. `(7sqrt(17))/3 cm`

Answer

B

Explanation

Fractional length hanging,
`l/L=(mu)/(1+mu)impliesl/30=0.5/(1+0.5) rArrl=10 cm`
let `'rho` be the mass per unit length. The coordinates of `20 rho` and `10 rho` are `(10,0)` and `(0,5)` respectively from `'A'`.
distance of `C.M` from `A,r_(cm)=sqrt(x_(cm)^(2)+y_(cm)^(2))`