Question

A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2Mg force. In this situation, tension in the string is x/5 Mg for x =__________. Neglect mass of the string and friction of the block (bigger mass) with ice slab.
(Given g = acceleration due to gravity)

Fig. Hanging mass

Answer 1

The correct answer is 6
$a = \frac{Mg}{4M + M }= \frac{g}{5}$
(in upward direction)
$T = M ( g + \frac{g}{5} ) = \frac{6Mg}{5}$
⇒ x = 6
Therefore , tension in the string is $\frac{x}{5}$ Mg for x = 6