Question

The work done $w$ by a body varies with displacement $x$ as $w=Ax+\frac{B}{{(c-x)}^2}$. The dimensional formula for 'B' is:

• A. ${ML}^2{T}^{-2}$
• B. ${ML}^4{T}^{-2}$
• C. ${MLT}^{-2}$
• D. ${ML}^2{T}^{-4}$

Answer 1

The correct option is B ${ML}^4{T}^{-2}$

$w=Ax+\frac{B}{{(c-x)}^2}$
$w=M^1{L}^2{T}^{-2}=\frac{B}{{(c-x)}^2}$
$\Rightarrow B=\left(M^1{L}^2{T}^{-2}\right)\left(L^2\right)$
$\Rightarrow B=M^1{L}^4{T}^{-2}$