Question

A physical quantity $A$ on multiplication with velocity results in another quantity $B$. If the quantity $B$ is energy, then the quantity $A$ is

• A. mass
• B. momentum
• C. force
• D. acceleration
• E. power

Answer 1

Answer: (B)

Given, $A \times v=B$
where, $B$ is energy.
$\Rightarrow A \times v=$ " Energy "
Dimensional formula of $v,[v]=\left[L T^{-1}\right]$
Dimensional formula of $E$,
$[E]=\left[M L^2 T^{-2}\right]$
Let dimensional formula of quantity $A=\left[M^a L^b T^c\right]$
$\Rightarrow\left[M^a L^b T^c\right]\left[L T^{-1}\right]=\left[M L^2 T^{-2}\right] $
$\Rightarrow\left[M^a L^{b+1} T^{c-1}\right]=\left[M L^2 T^{-2}\right]$
From the principle of homogeneity,
$ a=1$
$ b+1=2 \Rightarrow b=1 $
$ c-1=-2 \Rightarrow c=-1$
$ \Rightarrow \text { Dimensional formula of } A=\left[M L^0 T^{-1}\right] $
$ =\left[M L T^{-1}\right]$
This is the dimensional formula of momentum.