Consider the situation shown in figure. The force F is equal to the `(m_2g)/2`. If the area of cross section of the string is A and its Young modulus Y, find the strain developed in it. The string is light and there is no friction anywhere.

Answer

A, B

Explanation

From the ure `m_2g-T=m_2a……….1`
and `T-f=m_1a`…………….2

From eqn 1 and 2 we get
`a=(m_2g-F)/(m_1+m_2)`
`=(m_2g)/(2(m_1+m_2))`
Again `T=F+m_1a`
`rarr T=(m_2g)/2+m_1(m_2g)/(2(m_1+m_2))`
Now, `Y=(FL)/(A/_\\L)`
`rarr (/_\\\\L)/L=F/(AY)`
`rarr (/_\\\\L)/L=((m_2^2+2m_1m_2)g)/(2(m-1+m_2)AY)`
`=(m_2g(m_2+m_1))/(2AY(m_1+m_2))`