A block starts moving up an inclined plane of inclination 30 ° with an initial velocity of v 0 . It comes back to its initial position with velocity v 0 2 . The value of the coefficient of kinetic friction between the block and the inclined plane is close to 1 1000 , The nearest integer to I is :

Step-by-step solution

A   to   B a 1 = g   sin   30 ° + μg   cos   30 ° = g 2 + μg 3 2   ;   g = 10   m   s 2 v 0 2 - 2 a 1 s = 0 s = v 0 2 a 1 .....(i) B   to   A a 2 = g 2 - μ 3 2 g V 0 2 2 = 2 a 2 s s = V 0 2 4 a 2 .....(ii) From equation (i) and (ii) V 0 2 a 1 = V 0 2 4 a 2 ⇒       a 1 = 4 a 2 ⇒       5 + 5 3 μ = 4 5 - 5 3 μ ⇒       5 + 5 3 μ   ⇒ 25   3 &#9