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A rod AB of length 2 m and mass 2 kg is lying on smooth horizontal x- y plane with its centre at origin O as shown figure. An impulse J of magnitude 10 N to the power of negative s end exponent is applied perpendicular to AB at A. Co-ordinates of point A of the rod after time t = fraction numerator pi over denominator 45 end fraction s will be :-

  1. open square brackets open parentheses fraction numerator pi over denominator 9 end fraction plus fraction numerator square root of 3 over denominator 2 end fraction close parentheses m comma fraction numerator 1 over denominator 2 end fraction m close square brackets    
  2. open square brackets open parentheses fraction numerator 3 over denominator 4 end fraction m comma fraction numerator 3 over denominator 2 end fraction m close parentheses close square brackets    
  3. open square brackets open parentheses fraction numerator pi over denominator 6 end fraction plus fraction numerator 1 over denominator 2 end fraction close parentheses m comma fraction numerator 1 over denominator 2 end fraction m close square brackets    
  4. open square brackets fraction numerator 1 over denominator 2 end fraction m comma fraction numerator 1 over denominator 2 end fraction m close square brackets    

The correct answer is: open square brackets open parentheses fraction numerator pi over denominator 9 end fraction plus fraction numerator square root of 3 over denominator 2 end fraction close parentheses m comma fraction numerator 1 over denominator 2 end fraction m close square brackets

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A solid sphere has linear velocity v subscript 0 end subscript = 4 m/s and angular velocity omega subscript 0 end subscript =9 rad/s as shown. Ground on which it is moving, is smooth. It collides elastically with a rough wall of coefficient of friction mu. Radius of the sphere is 1 m and mass is 2 kg. What is net linear impulse imparted by the wall on the sphere during impact :-

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A solid sphere has linear velocity v subscript 0 end subscript = 4 m/s and angular velocity omega subscript 0 end subscript=9 rad/s as shown. Ground on which it is moving, is smooth. It collides elastically with a rough wall of coefficient of friction mu. Radius of the sphere is 1 m and mass is 2 kg. If the sphere after colliding with the wall roll without slipping in opposite direction, then coefficient of friction mu is :-

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