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Q.

A uniform disc of radius R rolls without slipping  on a rough horizontal surface.  At an instant, A is the lowest particle of the disc and C is the centre of disc. Then the location of particles on the disc at that instant, whose normal acceleration is zero, can be:

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a

Centre C of the disc

b

All particles on circle drawn on the disc plane with AC as diameter except A. 

c

All points on arc of a circle drawn with centre at A on disc and having radius R/2

d

No particle on disc has zero normal acceleration

answer is A, B.

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Detailed Solution

Take a point P on disc at a distance x from A, such that AP makes an angle  with vertical diameter of disc. Then the normal acceleration of P is  ω2xω2Rcosθ towards A.  Then the locus of points whose normal acceleration is zero are given by  x=Rcosθ. This is a circle with diameter AC

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A uniform disc of radius R rolls without slipping  on a rough horizontal surface.  At an instant, A is the lowest particle of the disc and C is the centre of disc. Then the location of particles on the disc at that instant, whose normal acceleration is zero, can be: