Question

A light rope fixed at one end of a wooden clamp on the ground passes over a tree branch and hangs on the other side (as per the figure). It makes an angle of ${30}^{\circ }$ with the ground. A man weighing (60 kg) wants to climb up the rope. The wooden clamp can come out of the ground if an upward force greater than 360 N is applied to it. Find the maximum acceleration in the upward direction with which the man can climb safely. Neglect friction at the tree branch. Take g = 10 m/$s^2$.

• A. 1
• B. 2
• C. 5
• D. 10

Answer 1

The correct option is B

2

Let 'T' be the tension in the rope. The upward force on the clamp is T sin ${30}^{\circ }=\frac{T}{2}$. The maximum tension that will not detach the clamp from the ground is, therefore, given by

$\frac{T}{2}=360N$

or, T = 720N

If the acceleration of the main in the upward direction is a, the equation of motion of the man is

T - 600N = (60kg)a

The maximum acceleration of the man for safe climbing is, therefore

$a=\frac{720N-600N}{60kg}=2m/s^2$