Physics-
General
Easy

Question

A T shaped object with dimension shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to A B, such that the object has only the translational motion without rotation. Find the location of P with respect to C.

  1. fraction numerator 2 over denominator 3 end fraction l    
  2. fraction numerator 3 over denominator 2 end fraction l    
  3. fraction numerator 4 over denominator 3 end fraction l    
  4. l    

The correct answer is: fraction numerator 4 over denominator 3 end fraction l


    For translator motion the force should be applied on the centre of mass of the body so we have to calculate the location of centre of mass of T shaped object.
    Let mass of rod A B is m so the mass of rod C D will be 2m.
    Let y subscript 1 end subscript is the centre of mass of rod A B and y subscript 2 end subscript is the centre of mass of rod C D. We can consider that whole mass of the rod is placed at their respective centre of mass i e, mass m is placed at y subscript 1 end subscript and mass 2 m is placed at y subscript 2 end subscript.
    Taking point c at the origin position vector of points y subscript 1 end subscript a n d blank y subscript 2 end subscript can be written as
    r subscript 1 end subscript equals 2 l j comma blank r subscript 2 end subscript equals l j
    and m subscript 1 end subscript equals m a n d m subscript 2 end subscript equals 2 m
    Position vector of centre of mass of the system
    r subscript C M end subscript equals fraction numerator m subscript 1 end subscript r subscript 1 end subscript plus m subscript 2 end subscript r subscript 2 end subscript over denominator m plus m subscript 2 end subscript end fraction equals fraction numerator m 2 l stack j with hat on top plus 2 m l stack j with hat on top over denominator m plus 2 m end fraction equals fraction numerator 4 m l stack j with hat on top over denominator 3 m end fraction equals fraction numerator 4 l stack j with hat on top over denominator 3 end fraction

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