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Standard X

Physics

Kinetic Energy

A disc of mas...

Question

A disc of mass $100 g$ and radius $10 c m$ has a projection on its circumference. The mass of projection is negligible. A $20 g$ bit of putty moving tangential to the disc with a velocity of $5 m s^{- 1}$ strikes the projection and sticks to it. The angular velocity of disc is

14.29 r a d s_{1}

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17.3 r a d s_1

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12.4 r a d s_1

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9.82 r a d s_{1}

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Solution

The correct option is A $14.29 r a d s_{1}$
In this case, the angular momentum of bit of putty about the axis of rotation = angular momentum of system of disc and bit of putty about the axis of rotation.

Let:
$M$ = Mass of puty
$m$ = Mass of disc
$∴ M v R = (\frac{m R^{2}}{2} + M R^{2}) ω$

$ω = \frac{M v R}{(\frac{m R^{2}}{2} + M R^{2})}$

Putting all the values

$ω = 14.298 m / s$

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A disc of mass 100 g and radius 10 cm has a projection on its circumference. The mass of projection is negligible. A 20 g bit of putty moving tangential to the disc with a velocity of 5 m s−1 strikes the projection and sticks to it. The angular velocity of disc is

A disc of mass $100 g$ and radius $10 c m$ has a projection on its circumference. The mass of projection is negligible. A $20 g$ bit of putty moving tangential to the disc with a velocity of $5 m s^{- 1}$ strikes the projection and sticks to it. The angular velocity of disc is