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An equation connecting different physical quantities is given below.

X=(Y+Z)PQ+KPQ where X denote force..
A) Find the dimension of K if the dimension of Y is M°L^3T°
C) In the above equation, the dimension of Q is M°LT^-2. Can you suggest a physical quantity which denotes P.?



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X = force = M L T^-2

X  =  (Y+Z) P Q + K P Q
  = Y P Q + Z P Q + K P Q
   = (Y + Z + K) * P * Q

Y , K, Z have all same dimensions.  since  they are arithmetically added.
   so  K has dimensions  L^3

Q = L T^-2
K P Q = has same dimensions as X = M L T^-2
  [L^3] P  [ L T^-2]  =  M L T^-2

    =>   P = M L^-2 =  mass per unit area

         P can also be the linear mass density variation with width or length. (rate of change in x or y direction)

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