Two blocks of masses m and 2 m are connected by a light inextensible string passing over a smooth fixed pulley. The system is released from rest. What is the acceleration of the center of mass of the

Question

Two blocks of masses m and 2 m are connected by a light inextensible string passing over a smooth fixed pulley. The system is released from rest. What is the acceleration of the center of mass of the two-block system?

TestHub · Accepted Answer

First, find the acceleration of the individual blocks. For an Atwood machine, the acceleration is $a = \frac{( m _{2} - m _{1} ) g}{m _{1} + m _{2}}$ . Here, $m_{1} = m$ and $m_{2} = 2 m$ . So, $a = \frac{( 2 m - m ) g}{m + 2 m} = \frac{m g}{3 m} = \frac{g}{3}$ .

Let the mass $2 m$ move downwards (acceleration $- a \hat{j}$ ) and mass $m$ move upwards (acceleration $+ a \hat{j}$ ). The acceleration of the center of mass is given by: $A_{CM} = \frac{m _{1} a _{1} + m _{2} a _{2}}{m _{1} + m _{2}}$ $A_{CM} = \frac{m ( a j ^ ) + 2 m ( - a j ^ )}{m + 2 m} = \frac{ma j ^ - 2 ma j ^}{3 m} = \frac{- ma j ^}{3 m} = - \frac{a}{3} \hat{j}$ Substitute $a = g /3$ : $A_{CM} = - \frac{( g /3 )}{3} \hat{j} = - \frac{g}{9} \hat{j}$ . The magnitude of the acceleration of the center of mass is $\frac{g}{9}$ .

Physics - Center of Mass Question with Solution | TestHub

Options:

Doubts & Discussion

JEE Main 2028 (Class 11)