# Laws motin qution

Let m1 = 8 kg, m2 = 12 kg and tension in string = T

Mass m2 being heavy will move down with acceleration and mass m1 will move upward.

Applying Newtons second law of motion to each mass:

>For mass m1:

The equation of motion will be:

T – m1xg = ma …(i)

>For mass m2:

The equation of motion will be:

m2xg – T = m2xa …(ii)

Adding (i) & (ii),

(m2 – m1)g = (m1 + m2)a

a=[(m2 – m1)/(m1 + m2)g] …(iii)

= [(12 – 8)/(12 + 8) 10]

= 2 m/s^2

Therefore, acceleration of masses is 2 m/s^2

Now, substituting value of a in (ii),

m2xg – T = m2[(m2 – m1)/(m1 + m2)]g

T = [m2 – (m2^2 – m1 x m2)/(m1 + m2)]g

= [(2 x m1 x m2)/(m1 + m2)]g

= [(2 x 12 x 8)/(12 + 8)] x 10

= 96 N

Hence, the tension in the string is 96 N.