Sixteen beads in a string are placed on a smooth inclined plane to inclination θ = 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 be

Question

Sixteen beads in a string are placed on a smooth inclined plane to inclination θ = 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 vertex is g /2 . Value of N is

TestHub · Accepted Answer

For the n hanging beads: nm g − T = nm 2 g ​ , so T = 2 nm g ​ For the 16 − n beads on the incline: T − ( 16 − n ) m g sin θ = ( 16 − n ) m 2 g ​ , with sin θ = 3 1 ​ 2 nm g ​ = ( 16 − n ) 6 5 m g ​ 3 n = 5 ( 16 − n ) , so n = 10 hang vertically and N = 16 − 10 = 6

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