Question

If the total energy of th eparticle is $E$, it will perform periodic motion only if

• A. $V_0>E>0$
• B. $E<0$
• C. $E>0$
• D. $E>V_0$

Answer 1

The correct option is A $V_0>E>0$

For motion to be periodic, it must reverse its path i.e., $KE$ should become zero for a finite value of x.

$NowK+U=E$

$\Rightarrow K=E-U$

$U_{max}=V_0$

$\Rightarrow K_{min}>0\text{particle will escape}$

$So,E-V_0<0$

$\Rightarrow E<V_0$

$Also,E=K+U>0$

Correct answer is $\left(3\right)$