A pulley fixed with ceiling carries a string with blocks of mass m and 3m attached to its ends. The masses of string and pulley are negligible. When the system is released, its centre of mass moves with acceleration

Question

A pulley fixed with ceiling carries a string with blocks of mass m and 3m attached to its ends. The masses of string and pulley are negligible. When the system is released, its centre of mass moves with acceleration (A) g (B) (g/5) (C) (g/4) (D) zero

Tardigrade Admin · Accepted Answer

The magnitude of the acceleration of each mass with respect to the pulley

a = \frac{3 m g - m g}{( 3 m + m )} = \frac{g}{2}

Acceleration of centre of mass

= \frac{( 3 m ) g /2 - m g /2}{( 3 m + m )} = \frac{g}{4}

Q. A pulley fixed with ceiling carries a string with blocks of mass $m$ and $3 m$ attached to its ends. The masses of string and pulley are negligible. When the system is released, its centre of mass moves with acceleration

$g$

$\frac{g}{5}$

$\frac{g}{4}$

zero

The magnitude of the acceleration of each mass with respect to the pulley
$a = \frac{3 m g - m g}{( 3 m + m )} = \frac{g}{2}$

Acceleration of centre of mass $= \frac{( 3 m ) g /2 - m g /2}{( 3 m + m )} = \frac{g}{4}$

Q. A pulley fixed with ceiling carries a string with blocks of mass m and 3m attached to its ends. The masses of string and pulley are negligible. When the system is released, its centre of mass moves with acceleration

g

5g​

4g​

zero

The magnitude of the acceleration of each mass with respect to the pulley a=(3m+m)3mg−mg​=2g​ Acceleration of centre of mass =(3m+m)(3m)g/2−mg/2​=4g​

Q. A pulley fixed with ceiling carries a string with blocks of mass $m$ and $3 m$ attached to its ends. The masses of string and pulley are negligible. When the system is released, its centre of mass moves with acceleration

$g$

$\frac{g}{5}$

$\frac{g}{4}$

The magnitude of the acceleration of each mass with respect to the pulley
$a = \frac{3 m g - m g}{( 3 m + m )} = \frac{g}{2}$

Acceleration of centre of mass $= \frac{( 3 m ) g /2 - m g /2}{( 3 m + m )} = \frac{g}{4}$