Question

Two masses are 8kg and 12 kg connected at the two ends of a light in-extensible string that goes over a frictionless pulley.Find the acceleration of the masses and the tension in the string when the masses are released.

Answer 1

Equation of motion for the 8kg mass:

$T-mg=ma$

$T-(8\times 10)=8a$

$T=8a+80$ ..(1)

Equation of motion for 12 kg mass:

$Mg-T=Ma$

$12\times 10-T=12a$

$120-(8a+80)=12a$

$40=20a$

$a=2m/s^2$

From(1), $T=8\times 2+80=96N$