Question

Assertion: when diver dives, the rotational kinetic energy of the diver increases during several somersaults.
Reason: When diver pulls his limbs, the moment of inertia decreases and on the account of conversion of angular momentum his angular speed increases.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect

Answer 1

Hint:Use conservation of angular momentum to solve this problem. The conservation of angular momentum states that the angular momentum of a system is conserved at any instant of time if any external torque is not applied to the system.

Formula used:
The conservation of angular momentum is given by,
\[L = I\omega = k\]
where \[L\] is the angular momentum of the body \[I\] is the moment of inertia of the body \[\omega \] is the angular velocity of the body and \[k\] is some constant.

Complete step by step answer:
When a diver dives it is said in the question that the rotational kinetic energy of the diver increases during several somersaults. When a diver dives the external torque acting on the diver is zero. Hence, the angular momentum of the diver is conserved.

Now, let’s say at the point of jump the moment of inertia of the diver is \[{I_1}\] and the angular momentum of the diver is \[{\omega _1}\] and when the diver pulls his limbs the moment of inertia of the diver is \[{I_2}\] and the angular momentum of the diver is \[{\omega _2}\]. So, we can write, \[{I_1}{\omega _1} = {I_2}{\omega _2}\].

Now, when the diver pulls his limbs the radius of its rotation decreases and the mass concentrates on the axis of rotation hence the moment of inertia decreases.
\[{I_1} > {I_2}\]
So, from conservation of angular momentum the angular velocity increases.
\[{\omega _1} < {\omega _2}\]
Also, since the angular speed increases rotational kinetic energy also increases. Hence, the angular speed or velocity of the diver increases. Hence, Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

Hence, option A is the correct answer.

Note: The rotational kinetic energy of a rotating body is given by, \[\dfrac{1}{2}I{\omega ^2}\]. So, when the moment of inertia decreases and the angular speed increases the increase in angular speed increases the kinetic energy with the square of it. So, net kinetic energy increases when the moment of inertia decreases.