Search any question & find its solution
Question:
Answered & Verified by Expert
An object executes SHM along $x$-axis with amplitude $0.06 \mathrm{~m}$. At certain distance ' $x$ ' metre from mean position, it has kinetic energy $10 \mathrm{~J}$ and potential energy $8 \mathrm{~J}$. The distance ' $\mathrm{x}$ ' will be
Options:
Solution:
1715 Upvotes
Verified Answer
The correct answer is:
0.04 m
$\begin{aligned} & \mathrm{A}=0.06 \mathrm{~m}, \mathrm{~K} . \mathrm{E} .=10 \mathrm{~J}, \mathrm{P} . \mathrm{E} .=8 \mathrm{~J} \\ & \text { Total energy T.E. }=10+8=18 \mathrm{~J} \\ & \text { P.E. }=\frac{1}{2} \mathrm{kx}^2, \mathrm{TE}=\frac{1}{2} \mathrm{kA}^2 \\ & \therefore \frac{\mathrm{P} . \mathrm{E}}{\mathrm{T} . \mathrm{E}}=\frac{\mathrm{x}^2}{\mathrm{~A}^2}=\frac{8}{18}=\frac{4}{9} \\ & \therefore \frac{\mathrm{x}}{\mathrm{A}}=\frac{2}{3} \text { or } \mathrm{x}=\frac{2}{3} \mathrm{~A}=\frac{2}{3} \times 0.06=0.04 \mathrm{~m}\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.