Two spheres of masses 2.6 kg and 4.1 kg are tied together by a light string looped over a frictionless pulley.
(i) What will the acceleration of each mass be?
(ii) Find the value of tension in the string.

Explanation

Here, `m_(1)=2.6kg, m_(2)=4.1 kg`

FBD for `m_(1)`
`T-m_(1)g =m_(1)a`
`T-2.6g=2.6a`……….(i)
FBD for `m_(2)`
`m_(2)g-T=m_(2)a` (downward)
4.1g -T=4.1a ……(ii)
Adding Eqs. (i) and (ii) we get
`4.1g-2.6g=(2.6+4.1)a`
`a=(1.52g)/(6.7)=(1.5xx10)/(6.7)=2.2 ms^(-2)`
Putting the value of a in Eq. (i), we get
`T-2.6g=2.6xx2.2`
`T=2.6xx2.2+2.6xx10`
=31.72N