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If P represents radiation pressure, C represent speed of light and Q represents radiation energy striking a unit area per second, then the non-zero integers, x,y and z such that P^(x)Q^(y)C^(z) is dimensionless are : |
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Answer» `x=1,y=1,z=1` `c=[LT^(-1)]` and `Q=("ENERGY")/("area" xx "time")=(ML^(2)T^(-2))/(L^(2)T)=[ML^(0)T^(-3)]` Now `P^(x)Q^(y)C^(z)=[M^(x)L^(-x)T^(-2x)][M^(y)T^(-3y)][L^(z)T^(-z)]` `P^(x)Q^(y)C^(z)=M^(x+y)L^(-x+z)T^(-2x-3y-z)` `P^(x)Q^(y)C^(z)` to be DIMENSIONLESS. `x+y=0,-x+z=0,-2x-3y-z=0` Also it is given that `x,y,z` are to be non-zero `i.e` least value of `x` should be. `1`. Thus if `x=1,` then `y=-1` and `z=1` will satisfy the above equations. Therefore, we get `x=`,`y=-1` and `z=1`. Hence correct choice is `(d)`. |
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