MCQ
The potential energy of a particle executing S.H.M. is $ 2.5\, J$, when its displacement is half of amplitude. The total energy of the particle be .... $J$
- A$18$
- ✓$10$
- C$12$
- D$2.5$
✓
Answer
Correct option: B.
$10$
b
(b) $\frac{{{\rm{Potential\, energy (}}U{\rm{)}}}}{{{\rm{Total \,energy (}}E{\rm{)}}}} = \frac{{\frac{1}{2}m{\omega ^2}{y^2}}}{{\frac{1}{2}m{\omega ^2}{a^2}}} = \frac{{{y^2}}}{{{a^2}}}$
(b) $\frac{{{\rm{Potential\, energy (}}U{\rm{)}}}}{{{\rm{Total \,energy (}}E{\rm{)}}}} = \frac{{\frac{1}{2}m{\omega ^2}{y^2}}}{{\frac{1}{2}m{\omega ^2}{a^2}}} = \frac{{{y^2}}}{{{a^2}}}$
So $\frac{{2.5}}{E} = \frac{{{{\left( {\frac{a}{2}} \right)}^2}}}{{{a^2}}}$
==> $E = 10J$
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