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Standard XII

Physics

Instantaneous Velocity

The cylinder ...

Question

The cylinder of the radius r is confined to roll without slipping at A to B. If the plates have velocities shown, determine the angular velocity of the cylinder.

\frac{3 v}{2 R}

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\frac{6 v}{R}

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\frac{7 v}{R}

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\frac{9 v}{R}

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Solution

The correct option is A $\frac{3 v}{2 R}$
From similar triangle
$\frac{v}{2 r - x} = \frac{2 v}{x}$
$3 x = 4 r \Rightarrow x = \frac{4}{3} r$
Now, angular velocity is given as,
$ω = \frac{v}{r} = \frac{2 v}{\frac{4}{3} r} = \frac{6 v}{4 r} = \frac{3 v}{2 r}$

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The cylinder of the radius r is confined to roll without slipping at A to B. If the plates have velocities shown, determine the angular velocity of the cylinder.

The correct option is A 3v2RFrom similar trianglev2r−x=2vx3x=4r⇒x=43rNow, angular velocity is given as,ω=vr=2v43r=6v4r=3v2r

The correct option is A $\frac{3 v}{2 R}$
From similar triangle
$\frac{v}{2 r - x} = \frac{2 v}{x}$
$3 x = 4 r \Rightarrow x = \frac{4}{3} r$
Now, angular velocity is given as,
$ω = \frac{v}{r} = \frac{2 v}{\frac{4}{3} r} = \frac{6 v}{4 r} = \frac{3 v}{2 r}$