Question

what is the dimension of a ?If f=at+b where F=force​

Answer 1

GiveN :

• F = at + b

To FinD :

• Dimension of a

SolutioN :

As we know that :

The Dimension formula of Force is $\sf{[MLT^{-2}]}$

And, we are given. F = at + b

______________________

$\rightarrow \sf{F \: = \: at} \\ \\ \rightarrow \sf{[MLT^{-2}] \: = \: [T] a} \\ \\ \rightarrow \sf{a \: = \: \dfrac{[MLT^{-2}]}{[T]}} \\ \\ \rightarrow \sf{a \: = \: [MLT^{-3}]}$

• Dimension formula of a is $\sf{[MLT^{-3}]}$

$\rule{150}{0.5}$

$\rightarrow \sf{F \: = \: b} \\ \\ \rightarrow \sf{b \: = \: [MLT^{-2}]}$

• Dimension formula of b is $\sf{MLT^{-2}]}$