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The dimensions of a/b in the equation P...

The dimensions of `a/b` in the equation `P=(a-t^(2))/(bx)` where `P` is pressure, `x` is distance and `t` is time are

A

`[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)]`

Text Solution

Verified by Experts

The correct Answer is:
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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