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

Answer

6

Explanation

If n beads each of mass m are hanging vertically then `nmg - T = (nm) (g)/(2)`
`:. T = n ((mg)/(2))` .....(1)
Also, `T - (16 - n) mg sin theta = (16 - n) m ((g)/(2))`
`rArr n ((mg)/(2)) - (16 - n) mg sin theta`
`= (16 - n) ((mg)/(2))`
`rArr ((n)/(2)) - (16 - n) ((1)/(3)) = ((16 - n)/(2))`
`rArr (n)/(2) = (16 - n) (5)/(6)`
`:. n = 10 " " N = 16 - 10 = 6`