Question

A pulley is hinged at the centre and a massless thread is wrapped around it. The thread is pulled with a constant force F starting from rest. As the time increases:

• A. its angular velocity increases, but force on hinge remains constant.
• B. its angular velocity remains same, but force on hinge increases.
• C. its angular velocity increases and force on hinge increases.
• D. its angular velocity remains same and force on hinge is constant.

Answer 1

The correct option is A its angular velocity increases, but force on hinge remains constant.

• As the pulley is hinged so there is translation equilibrium so net force on pulley is zero.The force on the hinge is constant that is $F$ and it is constant.
  
• Net torque on the pulley is $R\times F$ which is constant.

So as the torque on the pulley is constant its angular velocity will keep on increasing with time.