Question

Suppose the kinetic energy of a body oscillating with amplitude $A$ and at a distance $x$ is given by $K=\frac{Bx}{x^2+A^2}$. The dimensions of $B$ are the same as that of :

• A. $\frac{work}{time}$
• B. $work\times distance$
• C. $\frac{work}{distance}$
  
• D. $work\times time$

Answer 1

Answer: (B)

$work\times distance$

In the given equation $K=\frac{Bx}{x^2+A^2}$ dimension of $x$ and $A$ are same, so $\left[K\right]=\left[\frac{Bx}{x^2}\right]=\left[\frac{B}{x}\right]$
$\therefore B=K\times x=K.E.\times distance=work\times distance$