Question

The potential energy of a particle moving along x-axis is given by $U=20+sin\left(4\pi x\right)$ where U is in J and x is in meter under the action of conservative force

• A. If total mechanical energy is 20 J, then at $X=\frac{7}{8}m$, particle is in equilibrium
  
  
• B. If total mechanical energy is 20 J, then at $X=\frac{7}{8}m$, particle is not in equilibrium
  
• C. If total mechanical energy is 20 J, then at $X=\frac{3}{8}m$, particle is in equilibrium
• D. If total mechanical energy is 20 J, then at $X=\frac{3}{8}m$, particle is not in equilibrium

Answer 1

Answer: (A), (C)

The correct options are
A If total mechanical energy is 20 J, then at $X=\frac{7}{8}m$, particle is in equilibrium


C If total mechanical energy is 20 J, then at $X=\frac{3}{8}m$, particle is in equilibrium

$U_{min}=20+sin\left(4\pi x\right)=-1$
$U_{min}=20-15=15J{K}_{max}=E-U_{min}=20-15=5J4\pi x=\frac{3}{2}\pi .\frac{7}{2}\pi \Rightarrow X=\frac{3}{8},\frac{7}{8}\dots \dots$