Question

The velocity of a particle depends upon time according to the relation $v=\alpha t+\beta /t+y$. The dimensions of $\alpha ,\beta$ and y will be :

• A. $L{T}^{-2},L,L{T}^{-1}$
• B. $L,L{T}^{-1},L{T}^{-2}$
• C. $L{T}^{-1},L,L{T}^{-2}$
• D. $L{T}^{-1},L,T^{-1}L$

Answer 1

Answer: (A)

$L{T}^{-2},L,L{T}^{-1}$

Since the unit of velocity is meter per second its dimensions are
$\left[L{T}^{-1}\right]$
In order to equate the given equation the dimensions on either sides should be equal to $\left[L{T}^{-1}\right]$
Given equation in dimensional form is
$\left[L{T}^{-1}\right]=\alpha \left[T^1\right]+\beta \left[T^{-1}\right]+y$
To obtain required dimensions we write equation as
$\left[L{T}^{-1}\right]=\left[L{T}^{-2}\right]\left[T^1\right]+\left[L\right]\left[T^{-1}\right]+\left[L{T}^{-1}\right]$
Comparing both equations we get
$\alpha =\left[L{T}^{-2}\right],\beta =\left[L\right],y=\left[L{T}^{-1}\right]$