Question

Sixteen connected beads in a string are placed on a smooth incline as shown in equilibrium. The number of beads lying along the incline are:

• A. 4
• B. 8
• C. 12
• D. none of these

Answer 1

Answer: (C)

12

Since the system is in equilibrium, the net pulling force along the incline downwards and the pulling force straight downwards of the beads will be the SAME. Let there be'x' beads left on the incline. Equating the pulling gravitational forces we get,
$\frac{x}{16}mgsin\theta =\frac{16-x}{16}mg$
or, $\frac{x}{3}=16-x$
or, $x=12$