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Q.

A plank P is moving with constant velocity V on a horizontal surface. A disc of radius R is rolling without slipping on the plank with a velocity V relative to the plank. Then radius of curvature of the trajectory of a point on the circumference of the ring when it is at position A, as viewed by an observer standing on the ground is

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a

8R

b

5R

c

9R

d

4R

answer is B.

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Detailed Solution

As viewed by an observer on the ground, velocity of A is given byV→A =V→C + V→A/C = V+V i^+ωRj^ =2vi^+vj^∴         VA =  2v2 +v2 = 5 VNow acceleration of A is given bya→A = a→C + a→A/C =  0  +  ω2Ri  =  v2R  i^∴     VA2ρ =  aA ⇒  5 v2ρ  =  v2R  ⇒  ρ =  5R
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