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. (a) `K_1=K_2`
B. (b) `K_1gtK_2`
C. (c) `K_1ltK_2`
D. (d) Data insufficient

Answer

C

Explanation

Work done by friction:
`W=(mumgcostheta)S=(mumgcostheta)(h)/(sin theta)=mumghcottheta`
Now `cot theta_1=cot30^@=sqrt3`
`cot theta_2=cot 60^@=1/sqrt3`
i.e., kinetic energy `(KE=mgh-W)` in first case will be less or `K_1ltK_2`.