In the system shown in figure all surface are smooth, string in massless and inextensible. Find:

(a) acceleration of the system
(b) tensionin the string and
(c ) tension in the spring if force constant of spring is k = 50 N/m (Take g = 10 `m//s^(2)`)

Explanation

(a) `3g-kx=3a` ........(1)
`2g+kx-t=2a` .....(2)
t=a .........(3)
`therefore` Acceleration of the system is `a=(50)/(6)ms^(-2)`
(b) Free body diagram of 1 kg block gives `T=m=(1)((50)/(6))N=(50)/(6)N`
(c) Free body diagram of 3 kg block given
`3-kx=` but ma `ma=3xx(50)/(6)=25N`
`x=(30-25)/(k)=(5)/(50)=0.1m=10cm`