Question

two bodies of mass 4kg and 2kg are tied to the ends of a string which pass over a light frictionless pulley. the mass are released and at rest.if g=9 then acceleration of their centre of mass is​

Answer 1

Answer:

1m/s²

Explanation:

Let T be the tension in string .

Mass m1= 4 kg accelerate upwards with acceleration a

mass m2 = 2 kg accelerate downwards with same acceleration a .

m1g- T = m1a ---(1)

T- m2g = m2a ---(2)

$(m_{1}g-m_{2} g) = (m_{1} + m_{2}) \\ (m_{1} - m_{2} ) g= (m_{1} + m_{2})a \\ a = \frac{(m_{1}-m_{2} )}{(m_{1} + m_{2})} \times g \\ a = \frac{4 - 2}{4 + 2} \times g \\ a = \frac{2}{6} \times g \\ a = \frac{g}{3}$

Acceleration of centre of mass

$a _{c} = \frac{m_{1}a-m_{2} a}{m_{1}a + m_{2} a} = \frac{(m_{1}-m_{2})a }{m_{1}+ m_{2} } \\ a _{c} = \frac{(m_{1}-m_{2}) }{m_{1}+ m_{2} } \times \frac{g}{3}$

putting values of mass

$a _{c} = \frac{(4 -2 )}{(4+2)} \times \frac{9}{3} = \frac{2}{6} \times 3 \\ = \frac{1}{3} \times 3 = \frac{3}{3} = 1$

therefore acceleration of their centre of mass is 1m/s²