Question

The potential energy of a particle of mass ‘m’ is given by U = $\frac{1}{2}k{x}^2$ for x < 0 and U = 0 for $x\ge 0$. If total
mechanical energy of the particle is E. Then its speed for positive value of ‘x’ is

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

Answer 1

The correct option is B $\sqrt{\frac{2E}{m}}$

At $x=\sqrt{\frac{2E}{K}}$
Potential energy $U=0[\because x>0]$
Total energy is purely kinetic
$\therefore E=\frac{1}{2}m{v}^2\Rightarrow v=\sqrt{\frac{2E}{m}}$