A partical is realeased from the top of two inclined rought surface of height `h` each. The angle of inclination of the two planes are `30^(@)` and `60^(@)` respectively. All other factors (e.g. coefficient of friction , mass of the block etc) are same in both the cases. Let `K_(1) and K_(2)` be the kinetic energy of the partical at the bottom of the plane in two cases. Then

Options

A. `K_(1) = K_(2)`
B. `K_(1) gt K_(2)`
C. `K_(1) lt K_(2)`
D. data insufficient

Answer

B

Explanation

Work done in frictioin is
`W = (mu mg cos theta) s`
`= (mu mg cos theta) ((h)/(sin theta)) M`
Now `cos theta_(1) = cos 30^(@) = sqrt3`
and `cos theta _(2) = cos 60^(@) = (1)/(sqrt3)`
`:. W_(1) lt W_(2)`
i.e., kineyic energy in first case will be less.
`(K = mgh - W)`
or `K_(1) lt K_(2)`
.