SATHEE: Rotational Motion Question 100

Rotational Motion Question 100

Question: A cylinder of mass (M) and radius (R) is rotating with an angular velocity $(ω)$ . If the radius of the cylinder is halved 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: B

Solution:

The moment of inertia $(I)$ of a cylinder 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 halved, the new moment of inertia $(I^{'})$ becomes

$(\frac{1}{2} M {(\frac{R}{2})}^{2}$ = $\frac{1}{8} M R^{2})$ .

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

$(I^{'} ω^{'} = I ω)$ .

Therefore,

$\frac{1}{8} M R^{2} ω^{'} = \frac{1}{2} M R^{2} ω$

Solving for $(ω^{'})$ , we get $(ω^{'} = \frac{ω}{2})$ .

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Rotational Motion Question 100

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

Options:

Answer:

Solution:

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