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Q.

A circular disc with  a groove  along  its diameter  is placed horizontally on  a rough  surface. A block  of mass  1 kg  is placed  as shown  .The co-efficient  of friction  between  the block  and all surfaces of  groove and horizontal  surface  in contact  is μ=25. The disc  has an acceleration of 25m/s2towards  left.  The acceleration (in m/s2) of the block  with respect  to disc  is 5x find the  x value (Given  cosθ=45,sinθ=35)

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Detailed Solution

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Applying pseudo –force ma and resolving it Applying  Fnet=mαx for x direction

 macosθ(f1+f2)=max

 mαcosθμN1μN2=mαx

 mαcosθμmαsinθμmg=mαx

αx=αcosθμαsinθμg

 =25×4525×25×3525×10=10m/s2

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