A cord is wound round the circumference of wheel of radius r. The… - Vidyadip

MCQ

A cord is wound round the circumference of wheel of radius $r$. The axis of the wheel is horizontal and the moment of inertia about it is $I. \,A$ weight $mg$ is attached to the cord at the end. The weight falls from rest. After falling through a distance $ 'h '$, the square of angular velocity of wheel will be ..... .

A
$\frac{2 mgh }{ I +2 mr ^{2}}$
✓
$\frac{2 mgh }{ I + mr ^{2}}$
C
$2 gh$
D
$\frac{2 gh }{ I + mr ^{2}}$

✓

Answer

Correct option: B.

$\frac{2 mgh }{ I + mr ^{2}}$

b
$mgh =\frac{1}{2} I \omega^{2}+\frac{1}{2} mv ^{2}$

$v =\omega r$

$mgh =\frac{1}{2} I \omega^{2}+\frac{1}{2} m \omega^{2} r ^{2}$

$\frac{2 mgh }{\left( I + mr ^{2}\right)}=\omega^{2}$

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