Question

A man of mass m is inside a box of same mass .The whole system is suspended with ideal strings and pulley as shown in above figure.The tension t1 in the string so as to keep the system in equilibrium is​

Answer 1

Given:

A man of mass m is inside a box of same mass. The whole system is suspended with ideal strings and pulley as shown in above figure.

To find:

The tension t1 in the string so as to keep the system in equilibrium is​

Solution:

From given, we have,

The mass of man = the mass of box = m

The magnitude of the weight of man and box acting downward = mg

As the 2nd pulley is an ideal pulley so the force acting on it will be zero, so we have, 2T2 = T1 .........(1)

For the system to be in equilibrium upward force should balance the downward.

Therefore, we have,

T1 + T2 = mg + mg - T2

T1 + 2T2 = 2mg

using (1), we have,

T1 + T1 = 2mg

2T1 = 2mg

T1 = mg  

Therefore, the tension T1 in the string so as to keep the system in equilibrium is​ mg.