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)
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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