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Question: A particle is moved in a circle with a constant angular velocity. Its angular momentum is L. If the ...

A particle is moved in a circle with a constant angular velocity. Its angular momentum is L. If the radius of the circle is halved keeping the angular velocity same, the angular momentum of the particle will become –

A

L4\frac{L}{4}

B

L2\frac{L}{2}

C

L

D

2L

Answer

L4\frac{L}{4}

Explanation

Solution

L = Iw\ L2L1\frac{L_{2}}{L_{1}} = I2I1\frac{I_{2}}{I_{1}} [Q w = const.]

or L2L1\frac{L_{2}}{L_{1}} =m(r2)2mr2\frac{m\left( \frac{r}{2} \right)^{2}}{mr^{2}} = 14\frac{1}{4}

L2 = L14\frac{L_{1}}{4}