A composite inclined plane has three different inclined surfaces `AB, BC` and `CD` of heights `1 m` each and coefficients of friction `(1)/(sqrt(3)), (1)/(sqrt(8))` and `(1)/(sqrt(15))` respectively. A particle given an initial velocity at `A` along `AB` transverses the inclined surfaces with uniform speed, reaches `D` in `5s`. The initial speed given is `("in" m//s)`

Options

A. `1.6`
B. 1.8
C. 2.4
D. 3

Answer

B

Explanation

We know that if the angle of inclination is `tan^(-1) mu` no resultant force acts on the body . `therefore " " AB = (1)/("sin" (tan^(-1) (1)/(sqrt3))) = 2m`
`BC = (1)/("sin" (tan^(-1) (1)/(sqrt8))) = 3m`
CD = `(1)/("sin" (tan^(-1) (1)/(sqrt15))) = 4m `
`therefore` ABCD = 9m , T = 5 s , v = 1.8 m/s