Question

If the man shown in the figure below starts pulling the string with a rate of 2 m/s² then work done by tension on the block in 2 seconds will be [Given M = 5 kg]

Answer 1

240 J

Answer 2

1. Acceleration of the block: The man pulls the string with an acceleration of $a = 2 \text{ m/s}^2$. Since the pulley is ideal and the string is inextensible, the block also accelerates upwards with the same acceleration $a = 2 \text{ m/s}^2$.
2. Tension in the string: Applying Newton's second law to the block of mass $M$, the net force is $T - Mg$. Thus, $T - Mg = Ma$, which gives the tension $T = M(g+a)$. Assuming $g = 10 \text{ m/s}^2$, $T = 5 \text{ kg} \times (10 \text{ m/s}^2 + 2 \text{ m/s}^2) = 5 \times 12 = 60 \text{ N}$.
3. Displacement of the block: The block starts from rest ($u=0$) and accelerates at $a = 2 \text{ m/s}^2$ for $t = 2 \text{ s}$. Using the kinematic equation $d = ut + \frac{1}{2}at^2$, the displacement is $d = (0)(2) + \frac{1}{2}(2)(2)^2 = 4 \text{ m}$.
4. Work done by tension: The work done by tension ($W$) is given by $W = T \times d$, as tension and displacement are in the same direction (upwards). Therefore, $W = 60 \text{ N} \times 4 \text{ m} = 240 \text{ J}$.