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  • The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25% more than the potential energy is: ________ cm.Option

The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25% more than the potential energy is: ________ cm.

Option: 1

2


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} & K . E=P . E+\frac{25}{100} \times P . E . \\ & K . E=P . E+\frac{1}{4} P . E \\ & K . E=\frac{5}{4} P . E \\ & \frac{1}{2} K\left(A^2-x^2\right)=\frac{5}{4} \times \frac{1}{2} K^2 \\ & 4\left(A^2-x^2\right)=5 x^2 \\ \end{aligned}

\begin{aligned} & 4 A^2-4 x^2=5 x^2 \\ & 9 x^2=4 A^2 \\ & x^2=\frac{4}{9} \times(3)^2 \\ & \therefore x= \pm 2 \end{aligned}

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