SATHEE: Rotational Motion Question 39

Rotational Motion Question 39

Question: A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $ω$ . Two objects each of mass m are attached gently to the opposite ends of diameter of the ring. The ring will now rotate with an angular velocity:

[AIPMT 1998]

Options:

A) $\frac{ω (M - 2 m)}{(M + 2 m)}$

B) $\frac{ω M}{(M + 2 m)}$

C) $\frac{ω M}{(M + m)}$

D) $\frac{ω (M + 2 m)}{M}$

Show Answer

Answer:

Correct Answer: B

Solution:

Angular momentum remains conserved in the universe.

According to conservation of angular momentum

$L =$ constant

or $l ω = c o n s t a n t$

$∴$ $l_{1} ω_{1} = l_{2} ω_{2}$

Initial moment of inertia

$l_{1} = M R^{2}$

and angular velocity

$ω_{1} = ω$

Hence, $l_{1} ω_{1} = M R^{2} ω$

When two objects of mass m are attached to opposite ends of a diameter, the final readings are

$l_{2} = M R^{2} + m R^{2} + m R^{2}$

$= (M + 2 m) R^{2}$

So, $l_{2} ω_{2} = (M + 2 m) R^{2} ω_{2}$ ….(iii)

$∴$ From Eqs.(i), (ii) and (iii)

$M R^{2} ω = (M + 2 m) R^{2} ω_{2}$

$\Rightarrow$ $ω_{2} = \frac{ω M}{M + 2 m}$

Rotational Motion Question 39

Question: A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $ω$ . Two objects each of mass m are attached gently to the opposite ends of diameter of the ring. The ring will now rotate with an angular velocity:

Options:

Answer:

Solution:

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Rotational Motion Question 39

Question: A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity ω . Two objects each of mass m are attached gently to the opposite ends of diameter of the ring. The ring will now rotate with an angular velocity:

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $ω$ . Two objects each of mass m are attached gently to the opposite ends of diameter of the ring. The ring will now rotate with an angular velocity: