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Question

A disc is rolling (without slipping) on a horizontal surface. C is its centre and Q and P are two points equidistant from C as shown in figure. Let vP, vQ and vC be the magnitude of velocities of points P, Q and C respectively, then

A
vQ>vC>vP
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B
vQ<vC<vP
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C
vQ=vP, vC=12vP

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D
vQ=vC=vP
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Solution

The correct option is A vQ>vC>vP

Since P and Q are equidistant from the centre C, so it's distance from the axis of rotation is also same i.e r


Considering rightwards as +ve x direction, the velocity of point P and Q on the disc can be written as:
vP=(vrω)^i
vQ=(v+rω)^i
vC=v ^i
Hence magnitude of the velocity is in order:
vP<vC<vQ

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