Question

Sixteen beads in a string are placed on a smooth inclined plane of inclination sin^-1 (1/3) such that some of them lie along the incline whereas the rest hang over the top of the plane. If acceleration at first bead is g/2, the arrangement of beads is that

• A. 12 hang vertically.
• B. 10 lie along inclined plane.
• C. 8 lie along inclined plan
• D. 10 hang vertically.

Answer 1

Answer: (D)

10 hang vertically.

Answer 2

If n balls each of mass m are hanging vertically then, nmg – T = nma = $\frac { \mathrm { nmg } } { 2 }$

or T = $\frac { \mathrm { nmg } } { 2 }$ ……. (i)

also T – (16 - n) mg sin θ

= (16 - n) mg/2

on $\frac { \mathrm { nmg } } { 2 }$ - (16 - n)mg $\frac { 1 } { 3 }$ = (16 - n) $\frac { \mathrm { mg } } { 2 }$

or n $\frac { 4 } { 3 } = \frac { 80 } { 6 }$

or n = $\frac { 80 } { 6 } \times \frac { 3 } { 4 }$ = 10