Question

If kinetic energy of a body is given as $k=Cx$ where $C$ is constant and $x$ is distance from origin then, dimensional formula for $C$ is

• A. $\left[ML{T}^{-1}\right]$
• B. $\left[MLT\right]$
• C. $\left[M^{\circ }{L}^2{T}^{-1}\right]$
• D. $\left[ML{T}^{-2}\right]$

Answer 1

The correct option is D $\left[ML{T}^{-2}\right]$

$K=cx\Rightarrow \frac{1}{2}m{v}^2=cx$
$\Rightarrow M{L}^2{T}^{-2}=\left[C\right]L^1\Rightarrow \left[C\right]=M{L}^1{T}^{-2}$