Sixteen beads in a string are placed on a smooth inclined plane to inclination `theta = sin^(-1) (1//3)` such that some of them lie along the incline whereas the rest hang over the top of the plane. If N beads lie along inclined plane then the acceleration of the bead just below vertiex is `g//2`. Value of N is

Options

A. `12` hang vertically
B. `10` lie along inclined plane
C. `8` lie along inclined plane
D. `4` hang vertically

Answer

D

Explanation

Let `n` beeds each of mass `m` are hanging vertically then
`a=(nmg-(16-n)mgsintheta)/(16m)=((n-4)g)/(12)=(g)/(2)rArr`
`2n-8=12rArrn=10`