Question

v = at + b/(t + c) + vâ is a dimensionally valid equation. Obtain the dimensional formula for a, b, c where v is velocity, t is time and vâ is initial velocity.

Answer 1

Answer:

Dimensional formula for a, b and c is $LT^{-2}$ ,Land T.

Explanation:

Since equation is given v = at + b/(t + c) + vâ.

we need to find the dimensional formula for a, b, and c.

The term at is also a velocity

at=v

a=v/t

we know the dimension of velocity =$LT^{-1}$

So, dimensional formula of a=$LT^{-2}$

The term $\frac{b}{t+c}$ is also a velocity so

$\frac{b}{t+c} =v$

as the denominator is t+c is a time, so dimensional formula of c is T.

Now $\frac{b}{T} =v$

so dimensional formula of b is L.

So dimensional formula for a, b and c is $LT^{-2}$ ,Land T.