Question

A particle performs uniform circular motion with angular momentum
L. If frequency of motion is doubled and kinetic energy is reduced to
half, the angular monentum becomes :
एक कण L कोणीय संवेग से एकसमान वृत्तीय गति करता है। यदि गति की
आवृत्ति को दुगुना और गतिज ऊर्जा को आधा कर दें, तो कोणीय संवेग होगा :
(1) 2L
(2) 4L
(3) L/2
(4) L/4
​

Answer 1

Answer:

We have,

Angular momentum = L = Iω

Where, I is the moment of inertia and ω is the angular velocity.

So frequency of revolution is, f = ω/2π

=> ω = 2πf

Kinetic energy, K = ½ Iω2 = ½ Lω = ½ (2πfL) = πfL …………..(1)

Now, frequency is doubled, so, let f/ = 2f = 2(ω/2π) = ω/π

The kinetic energy is halved, so, K/ = K/2 = ½ (πfL)

If L/ is the new angular momentum, then using (1) we can write,

K/ = πf/L/

=> ½ (πfL) = π(2f)L/

=> L/ = L/4

So, angular momentum becomes one fourth of its original value.