In the given figurethe wedge is fixed, pulley is frictionless and string is light. Surface AB is frictionless whereas AC is rough. If the block of mass 3m. Slides down. With conttant velocity, then the coefficient of friction between surface AC and the block is

Options

A. `(1)/(3)`
B. `(2)/(3)`
C. `(1)/(2)`
D. `(4)/(3)`

Answer

C

Explanation

If a moves down the incline by 1m, B shall move up `hv(1)/(2) m`
If the speed of B is v then the speed of A will be 2v.
From conservation of energy, Gain in KE = loss in PE
`(1)/(2) m_(A) (2v)^(2) +(1)/(2) m_(B)v^(2)=m_(A) g xx (3)/(5)-m_(B)g xx (1)/(2)`
soving we get `v = (1)/(2) sqrt((g)/(3))`