A block of mass m is attached to one end of a light string which is wrapped on a disc of mass 2m and radius R . The total length of the slack portion of the string is l . The block is released from rest. The angular velocity of the disc just after the string becomes taut is

Question

A block of mass m is attached to one end of a light string which is wrapped on a disc of mass 2m and radius R . The total length of the slack portion of the string is l . The block is released from rest. The angular velocity of the disc just after the string becomes taut is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-4eykhvbsrqwy.png" /> (A) √(gl/R2) (B) √(gl/2R2) (C) √(2gl/3R2) (D) √(3gl/2R2)

Tardigrade Admin · Accepted Answer

Using the principle of conservation of angular momentum, m√2 gl× R=[((2 m) R2/2) + (mR)2]× ω ⇒ ω =√(gl/2 R2)

Q. A block of mass $m$ is attached to one end of a light string which is wrapped on a disc of mass $2 m$ and radius $R$ . The total length of the slack portion of the string is $l$ . The block is released from rest. The angular velocity of the disc just after the string becomes taut is

$\frac{g l}{R ^{2}}$

$\frac{g l}{2 R ^{2}}$

$\frac{2 g l}{3 R ^{2}}$

$\frac{3 g l}{2 R ^{2}}$

Using the principle of conservation of angular momentum,
$m 2 g l \times R = [\frac{( 2 m ) R ^{2}}{2} + (m R)^{2}] \times ω$
$\Rightarrow ω = \frac{g l}{2 R ^{2}}$

Q. A block of mass m is attached to one end of a light string which is wrapped on a disc of mass 2m and radius R . The total length of the slack portion of the string is l . The block is released from rest. The angular velocity of the disc just after the string becomes taut is

R2gl​​

2R2gl​​

3R22gl​​

2R23gl​​