Solveeit Logo
Login

Question

Question: In the system of two masses m<sub>1</sub> and m<sub>2</sub> tied through a light string passing over...

In the system of two masses m1 and m2 tied through a light string passing over a smooth light pulley. Find the acceleration of COM. (Centre of mass).

A

(m1−m2)m1+m2g\frac { \left( m _ { 1 } - m _ { 2 } \right) } { m _ { 1 } + m _ { 2 } } g

B

(m1−m2)m1+m2g\frac { \left( m _ { 1 } - m _ { 2 } \right) } { m _ { 1 } + m _ { 2 } } g

C

(m1−m2)2 m1+m2 g\frac { \left( \mathrm { m } _ { 1 } - \mathrm { m } _ { 2 } \right) ^ { 2 } } { \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } } \mathrm {~g}

D

(m1−m2m1+m2)2g2\left( \frac { m _ { 1 } - m _ { 2 } } { m _ { 1 } + m _ { 2 } } \right) ^ { 2 } \frac { g } { 2 } x

Answer

(m1−m2)m1+m2g\frac { \left( m _ { 1 } - m _ { 2 } \right) } { m _ { 1 } + m _ { 2 } } g

Explanation

Solution

aCOM = m1a1+m2a2m1+m2\frac { m _ { 1 } a _ { 1 } + m _ { 2 } a _ { 2 } } { m _ { 1 } + m _ { 2 } } Note that a2 = -a1,

∴ aCOM = (m1−m2)a2m1+m2\frac { \left( m _ { 1 } - m _ { 2 } \right) a _ { 2 } } { m _ { 1 } + m _ { 2 } } and a1=(m1−m2)gm1+m2a _ { 1 } = \frac { \left( m _ { 1 } - m _ { 2 } \right) g } { m _ { 1 } + m _ { 2 } }

= (m1−m2)2 m1+m2 g\frac { \left( \mathrm { m } _ { 1 } - \mathrm { m } _ { 2 } \right) ^ { 2 } } { \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } } \mathrm {~g}