SATHEE: Rotational Motion Question 99

Rotational Motion Question 99

Question:A disc of mass (M) and radius (R) is rotating with an angular velocity $(ω)$ . If the radius of the disc is doubled keeping the mass same, what will be the new angular velocity?

Options:

A) $ω$

B) $\frac{ω}{2}$

C) $\frac{ω}{4}$

D) $2 ω$

Show Answer

Answer:

Correct Answer: C

Solution:

The moment of inertia $(I)$ of a disc about its axis is given by $(\frac{1}{2} M R^{2})$ .

According to the conservation of angular momentum $(L = I ω = constant)$ , if the radius is doubled, the new moment of inertia $(I^{'})$ becomes $(\frac{1}{2} M {(2 R)}^{2} = 2 M R^{2})$ .

Therefore, the new angular velocity $(ω^{'})$ must be such that $(I^{'} ω^{'} = I ω)$ .

Therefore, $2 M R^{2} ω^{'} = \frac{1}{2} M R^{2} ω$ .

Solving for $(ω^{'})$ , we get $(ω^{'} = \frac{ω}{4})$ .

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Rotational Motion Question 99

Question:A disc of mass (M) and radius (R) is rotating with an angular velocity (ω). If the radius of the disc is doubled keeping the mass same, what will be the new angular velocity?

Options:

Answer:

Solution:

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Question:A disc of mass (M) and radius (R) is rotating with an angular velocity $(ω)$ . If the radius of the disc is doubled keeping the mass same, what will be the new angular velocity?