(16)

Sol. This problem can be solved in two steps:

Step Ι : When the body is moving up on the inclined plane (shown in fig. A)

Here ¡ N = mg cos α

The acceleration of the body is

a 1 = – = – (g sin α + μ g cos α )

Let body is projected with speed ν 0 along the inclined plane (along the x-axis). After time t, body

reaches at point P ( ν = 0) (as shown in fig.B).

Let OP = s

s = t 1 = t 1

a 1 = ∴ ν 0 = – a 1 t 1

∴ s = –

∴ t 1 =

= ..........

Step ΙΙ : When the body starts to return from point P, the acceleration is

a 2 = (In fig.C)

= g sin α – μ g cos α

∴ s = a 2 t

∴ t 2 = = ....(ii)

According to the problem,

t 2 = η t 1 ,

Putting the value of t 1 and t 2 from equations (i) and (ii), we get

μ = tan α = 0.16 = k

than 100 k = 16 Ans.