Question

The potential energy of a particle of mass m free to move along the x-axis is given by U = (1/2)$k{x}^2$ for x < 0 and U = 0 for $x\ge 0$ (x denotes the x-coordinate of the particle and k is a positive constant). If the total mechanical energy of the particle is E, then its speed at x = $-\sqrt{2E/K}$ is

• A. Zero
• B. $\sqrt{\frac{2E}{m}}$
• C. $\sqrt{\frac{E}{m}}$
• D. $\sqrt{\frac{3E}{2m}}$

Answer 1

The correct option is A Zero

We know that,

$M.E.=KE+PE$

as $x=\sqrt{\frac{2E}{K}}\Rightarrow x<0.$

So, $U=\left(1/2\right)k{x}^2\Rightarrow U=1/2K\left(\frac{2E}{x}\right)$

$\Rightarrow U=E$ $[U=P.E.]$

It is given that,

$ME=E$

So, $E=KE+E$

$0=KE$

AS, $\frac{M{V}^2}{2}=KE,v=0$

Option $-A$ is correct