Question

The potential energy of a particle executing S.H.M. $25J$ , when its displacement is half of amplitude. The total energy of the particle is :

• A. $250J$
• B. $180J$
• C. $100J$
• D. $25J$

Answer 1

Answer: (C)

$100J$

According to the conservation of energy

$K.E.+P.E.=constant$

Then

$\frac{1}{2}m{v}^2+\frac{1}{2}K{x}^2=\frac{1}{2}K{A}^2$

At half amplitude i.e.$A=\frac{x}{2}$

$K.E.=\frac{3}{8}K{A}^2$

$P.E.=\frac{1}{8}K{A}^2$

$K.E.=3P.E.$

$T.E.=4P.E.$

Hence the total energy is$100J$