Question

The potential energy of a particle of mass m is given$U=\frac{1}{2}k{x}^2$ for x < 0 and U = 0 for $x\ge 0.$ if total mechanical energy of the particle is E, then its speed at $x=\sqrt{\frac{2E}{k}}$ is

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

Answer 1

The correct option is A $zero$

$V=\frac{1}{2}k{x}^2$

E= Energy

Conservation of energy-

$P.E+K.E=E$

$K.E=E-P.E$

$=E-\frac{1}{2}k{x}^2$

$K.E.atx=\sqrt{\frac{2E}{k}}$

$\Rightarrow E-\frac{1}{2}k\left(\frac{2E}{k}\right)=0$

So, speed is zero