Question

wo masses m₁ and m₂ (m₁ > m₂) are connected by massless flexible and inextensible string passed over massless and frictionless pulley. The acceleration of centre of mass is

• A. $\left( \frac { m _ { 1 } - m _ { 2 } } { m _ { 1 } + m _ { 2 } } \right) ^ { 2 } g$
• B. $\frac { m _ { 1 } - m _ { 2 } } { m _ { 1 } + m _ { 2 } } g$
• C. $\frac { m _ { 1 } + m _ { 2 } } { m _ { 1 } - m _ { 2 } } g$
• D. Zero

Answer 1

Answer: (A)

$\left( \frac { m _ { 1 } - m _ { 2 } } { m _ { 1 } + m _ { 2 } } \right) ^ { 2 } g$

Answer 2

Acceleration of each mass $= a = \left( \frac { m _ { 1 } - m _ { 2 } } { m _ { 1 } + m _ { 2 } } \right) g$

Now acceleration of centre of mass of the system

$A _ { c m } = \frac { m _ { 1 } \overrightarrow { a _ { 1 } } + m _ { 1 } \overrightarrow { a _ { 2 } } } { m _ { 1 } + m _ { 2 } }$

As both masses move with same acceleration but in opposite direction so $\overrightarrow { a _ { 1 } } = - \overrightarrow { a _ { 2 } }$ = a (let)

$\therefore A _ { c m } = \frac { m _ { 1 } a - m _ { 2 } a } { m _ { 1 } + m _ { 2 } }$

$= \left( \frac { m _ { 1 } - m _ { 2 } } { m _ { 1 } + m _ { 2 } } \right) \times \left( \frac { m _ { 1 } - m _ { 2 } } { m _ { 1 } + m _ { 2 } } \right) \times g$

$= \left( \frac { m _ { 1 } - m _ { 2 } } { m _ { 1 } + m _ { 2 } } \right) ^ { 2 } \times g$