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A light straight fixed at one end to a wooden clamp on a ground passes over a fixed pulley and hangs at the other side. It makes an angle 30⁰ with the ground. A boy weighing 60 kg climbs up the rope. The wooden clamp can tolerate upto vertical force 360N. Find the, maximum acceleration in the upward direction with which the boy can climb safely. The friction of pulley and wooden clamp may be ignored (g = 10 m/s²)

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$3 m / s^{2}$

$4 m / s^{2}$

$2 m / s^{2}$

$1 m / s^{2}$

answer is B.

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Detailed Solution

For the boy,

T - mg = ma

For the clamp,

max vertical force = 360N
Vertical force on the clamp = Tsin(30) = T/2 = 360

T_max = 720N

Therefore, ma = 720 - (60)(10) = 120

a = 120/60 = 2 $m / s^{2}$

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