A pulley having some mass has a massless string around it, with two unequal masses at the end of the string. Sufficient friction is present between pulley and the string such that the string does not slip on the pulley .
The tensions in the massless string on the two sides of pulley will be same or different?
According to me the tensions on the two sides should be different so as to provide a net torque to the pulley .But what I have learned till now is that the tension in a massless string is same throughout.
Let the tensions on the two sides of the string be $T_1$ and $T_2$.
Writing equation for rotational motion of pulley we have (T1-T2)R = Ia
Since the pulley has non zero moment of inertia and angular acceleration ,T1 WILL NOT BE EQUAL TO T2.
I am having difficulty in understanding that how can a massless string have different tensions.