Question

The potential energy of particle of mass m free to move along X-axis is given by $U=\frac{1}{2}K{X}^{2}forX<0andU=0forX>0$ {X denotes the X-coordinate of the particle and K is a positive constant ] If the 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

Given that

Total mechanical energy of particle is, $T=E$

Potential energy of particle , $U=\frac{1}{2}K{X}^2$ for $X<0$

where $X$ is coordinate of particle

At $X=-\sqrt{\frac{2E}{K}}$

Potential energy ,$U=\frac{1}{2}K(-\sqrt{\frac{2E}{K}}{)}^2=E$

Since $T=E$

$⟹U+\text{Kinetic energy}=E$

$⟹\text{Kinetic energy at}X=-\sqrt{\frac{2E}{K}}is0$

$\therefore$ Velocity at $X=-\sqrt{\frac{2E}{K}}$ is zero