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Q.

A uniform plate of length a = 0.6 m and width b = 0.4 m having mass M = 3 kg is free to rotate about an edge. Initially the plate is kept horizontally and small particles each of mass  M = 0.01 kg collide elastically and perpendicular to the plate on the second half of the plate at the rate n = 100 particles per unit time per unit area as shown. What will be the velocity of striking particles so that plate does not rotate ?

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a

85.4 m/s

b

81.2  m/s

c

83.3 m/s

d

79.3 m/s

answer is C.

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Detailed Solution

The force exerted by the particles = 2 n m v per unit area

Total force exented      F  =  2mnv×a2×b      = 2×100×0.01×v×0.3×0.4      = 0.24 v

This force acts at a distance of  x= 0.3 +0.32    = 0.45 m

For the rotational equilibrium of the plate, we have

τweight         =   τforce 3g×0.3  =   F × 0.45                    = 0.24 V×0.45         v     = 83.3 m/s

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