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Standard XII

Physics

Rotation + Translation

A uniform dis...

Question

A uniform disc of mass m and radius R is projected horizontally with velocity $v_{0}$ on a rough horizontal floor, so that it starts off with a purely sliding motion at t=0. After $t_{0}$ seconds, it acquires a purely rolling motion as shown in figure.

Calculate the velocity of the centre of mass of the disc at $t_{0}$ .

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Assuming the coefficient of friction to be $μ$ , calculate $t_{0}$ . Also calculate the work done by the frictional force as a function of time and the total work done by it over a time t much longer than $t_{0}$ .

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$v = \frac{2}{3} v_{0}$

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$z_{o} = \frac{v_{o}}{3 m g}$

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Solution

The correct option is D
$z_{o} = \frac{v_{o}}{3 m g}$

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A uniform disc of mass m and radius R is projected horizontally with velocity v0 on a rough horizontal floor, so that it starts off with a purely sliding motion at t=0. After t0 seconds, it acquires a purely rolling motion as shown in figure.

The correct option is D zo=vo3mg Watch the next video for the solution.

A uniform disc of mass m and radius R is projected horizontally with velocity $v_{0}$ on a rough horizontal floor, so that it starts off with a purely sliding motion at t=0. After $t_{0}$ seconds, it acquires a purely rolling motion as shown in figure.

The correct option is D
$z_{o} = \frac{v_{o}}{3 m g}$

Watch the next video for the solution.