1.

The dimensions of `a/b` in the equation `P=(a-t^(2))/(bx)` where `P` is pressure, `x` is distance and `t` is time areA. `[M^(1)L^(1)T^(-2)]`B. `[M^(0)L^(2)T^(-2)]`C. `[M^(1)L^(1)T^(1)]`D. `[M^(1)L^(0)T^(-2)]`

Answer» Correct Answer - d
`P=(a-t^(2))/(bx)=(a)/(bx)-(t^(2))/(bx)`
According to principle of homogeneity of dimensions, each term should have the same dimensions.
`therefore [P]=[(a)/(bx)] therefore [("Force")/("Area")]=[(a)/(b)xx(1)/(x)]`
`therefore [(M^(1)L^(1)T^(-2))/(L^(1)xxL^(1))]=[(a)/(b)xx(1)/(L)]`
`therefore [(a)/(b)]=[M^(1)L^(-1)T^(-2)xxL^(1)]=[M^(1)L^(0)T^(-2)]`


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