Torsional spring and maximum velocity of wheel

[surya teja saithana]

Moderator's Note: HOMEWORK POSTED IN WRONG THREAD, SO NO TEMPLATE
Thread title changed to make it descriptive of the problem.

can i solve this question using energy conservation method as shown.

 

[gneill]

Your work and result look good to me.

I would probably have skipped the calculus myself, realizing that the wheel would be accelerating so long as the torque applied by the spring was positive and so transferring energy from the spring to the wheel. Hence the energy transfers from the spring to the wheel until the net rotation returns to zero, whereupon all the spring PE has moved to the wheel KE.