GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

Question : 14 of 65

Marks: +1, -0

A circular disk of radius

r

is confirmed to roll without slipping at

P

and

Q

as shown in the figure.

If the plates have velocities as shown, the magnitude of the angular velocity of the disk is

Solution:

Instantaneous centre will be at intersection of perpendiculars of velocity vector.
Let IC be at a distance = x from point P.
Thus,

\;{V}/{x}=\;{2 V}/{2 r-x}

2 V r-V x=2 V x

2 V r=3 V x

x=\;{2 r}/{3}

Thus,

V=x ω

{V}=\;{2 r}/{3} ω

ω=\;{3 {V}}/{2 r}

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