Question

The potential energy of a particle executing S.H.M. is $2.5J$, when its displacement is half of amplitude. The total energy of the particle be:-

• A. $18J$
• B. $10J$
• C. $12J$
• D. $2.5J$

Answer 1

Answer: (B)

$10J$

As we know,

$\frac{Potentialenergy\left(U\right)}{Totalenergy\left(E\right)}=\frac{\frac{1}{2}m{\omega }^2{y}^2}{\frac{1}{2}m{\omega }^2{a}^2}=\frac{y^2}{a^2}$
So

$\frac{2.5}{E}=\frac{{\left(\frac{a}{2}\right)}^2}{a^2}\Rightarrow E=10J$