364086
When a spring is stretched by \(10\;cm\), the potential energy stored is \(E\). When the spring is stretched by \(10\;cm\) more, the potential energy stored in the spring becomes
1 \(2\,E\)
2 \(4\,E\)
3 \(6\,E\)
4 \(10\,E\)
Explanation:
We get \(E=\dfrac{1}{2} K(10)^{2}\) \(\begin{aligned}E_{2} & =\dfrac{1}{2} K(20)^{2} \\& =\dfrac{1}{2} K \times 4 \times 10^{2} \\E_{2} & =4 E\end{aligned}\)
PHXI14:OSCILLATIONS
364087
Assertion : In a SHM, kinetic and potential energies become equal when the displacement is \(1 / \sqrt{2}\) times the amplitude. Reason : In SHM, kinetic energy is zero when potential energy is maximum.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
\(E_{k}=\dfrac{1}{2} m \omega^{2}\left(A^{2}-x^{2}\right)\) \(U=\dfrac{1}{2} m \omega^{2} x^{2}\) When \(x=\dfrac{A}{\sqrt{2}}\), then \(E_{k}=U\) When \(x=0, U=U_{\text {min }}=0\) and \(E_{k}=\left(E_{k}\right)_{\max }=\dfrac{m \omega^{2} A^{2}}{2}\) So correct option is (2).
PHXI14:OSCILLATIONS
364088
A particle of mass \(1 \mathrm{~kg}\) is undergoing S.H.M., for which graph between force and displacement (from mean position) is shown. Its time period, in seconds, is:
1 \(\pi / 3\)
2 \(2 \pi / 3\)
3 \(\pi / 6\)
4 \(3 / \pi\)
Explanation:
\(F=-m \omega^{2} x\) so \(\omega^{2}=\dfrac{13.5}{1.5}=9\) \(\Rightarrow \omega=3\) \(\Rightarrow T=\dfrac{2 \pi}{3}\)
PHXI14:OSCILLATIONS
364089
The amplitude of a simple harmonic oscillator is doubled. Which of the following is doubled?
NEET Test Series from KOTA - 10 Papers In MS WORD
WhatsApp Here
PHXI14:OSCILLATIONS
364086
When a spring is stretched by \(10\;cm\), the potential energy stored is \(E\). When the spring is stretched by \(10\;cm\) more, the potential energy stored in the spring becomes
1 \(2\,E\)
2 \(4\,E\)
3 \(6\,E\)
4 \(10\,E\)
Explanation:
We get \(E=\dfrac{1}{2} K(10)^{2}\) \(\begin{aligned}E_{2} & =\dfrac{1}{2} K(20)^{2} \\& =\dfrac{1}{2} K \times 4 \times 10^{2} \\E_{2} & =4 E\end{aligned}\)
PHXI14:OSCILLATIONS
364087
Assertion : In a SHM, kinetic and potential energies become equal when the displacement is \(1 / \sqrt{2}\) times the amplitude. Reason : In SHM, kinetic energy is zero when potential energy is maximum.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
\(E_{k}=\dfrac{1}{2} m \omega^{2}\left(A^{2}-x^{2}\right)\) \(U=\dfrac{1}{2} m \omega^{2} x^{2}\) When \(x=\dfrac{A}{\sqrt{2}}\), then \(E_{k}=U\) When \(x=0, U=U_{\text {min }}=0\) and \(E_{k}=\left(E_{k}\right)_{\max }=\dfrac{m \omega^{2} A^{2}}{2}\) So correct option is (2).
PHXI14:OSCILLATIONS
364088
A particle of mass \(1 \mathrm{~kg}\) is undergoing S.H.M., for which graph between force and displacement (from mean position) is shown. Its time period, in seconds, is:
1 \(\pi / 3\)
2 \(2 \pi / 3\)
3 \(\pi / 6\)
4 \(3 / \pi\)
Explanation:
\(F=-m \omega^{2} x\) so \(\omega^{2}=\dfrac{13.5}{1.5}=9\) \(\Rightarrow \omega=3\) \(\Rightarrow T=\dfrac{2 \pi}{3}\)
PHXI14:OSCILLATIONS
364089
The amplitude of a simple harmonic oscillator is doubled. Which of the following is doubled?
364086
When a spring is stretched by \(10\;cm\), the potential energy stored is \(E\). When the spring is stretched by \(10\;cm\) more, the potential energy stored in the spring becomes
1 \(2\,E\)
2 \(4\,E\)
3 \(6\,E\)
4 \(10\,E\)
Explanation:
We get \(E=\dfrac{1}{2} K(10)^{2}\) \(\begin{aligned}E_{2} & =\dfrac{1}{2} K(20)^{2} \\& =\dfrac{1}{2} K \times 4 \times 10^{2} \\E_{2} & =4 E\end{aligned}\)
PHXI14:OSCILLATIONS
364087
Assertion : In a SHM, kinetic and potential energies become equal when the displacement is \(1 / \sqrt{2}\) times the amplitude. Reason : In SHM, kinetic energy is zero when potential energy is maximum.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
\(E_{k}=\dfrac{1}{2} m \omega^{2}\left(A^{2}-x^{2}\right)\) \(U=\dfrac{1}{2} m \omega^{2} x^{2}\) When \(x=\dfrac{A}{\sqrt{2}}\), then \(E_{k}=U\) When \(x=0, U=U_{\text {min }}=0\) and \(E_{k}=\left(E_{k}\right)_{\max }=\dfrac{m \omega^{2} A^{2}}{2}\) So correct option is (2).
PHXI14:OSCILLATIONS
364088
A particle of mass \(1 \mathrm{~kg}\) is undergoing S.H.M., for which graph between force and displacement (from mean position) is shown. Its time period, in seconds, is:
1 \(\pi / 3\)
2 \(2 \pi / 3\)
3 \(\pi / 6\)
4 \(3 / \pi\)
Explanation:
\(F=-m \omega^{2} x\) so \(\omega^{2}=\dfrac{13.5}{1.5}=9\) \(\Rightarrow \omega=3\) \(\Rightarrow T=\dfrac{2 \pi}{3}\)
PHXI14:OSCILLATIONS
364089
The amplitude of a simple harmonic oscillator is doubled. Which of the following is doubled?
364086
When a spring is stretched by \(10\;cm\), the potential energy stored is \(E\). When the spring is stretched by \(10\;cm\) more, the potential energy stored in the spring becomes
1 \(2\,E\)
2 \(4\,E\)
3 \(6\,E\)
4 \(10\,E\)
Explanation:
We get \(E=\dfrac{1}{2} K(10)^{2}\) \(\begin{aligned}E_{2} & =\dfrac{1}{2} K(20)^{2} \\& =\dfrac{1}{2} K \times 4 \times 10^{2} \\E_{2} & =4 E\end{aligned}\)
PHXI14:OSCILLATIONS
364087
Assertion : In a SHM, kinetic and potential energies become equal when the displacement is \(1 / \sqrt{2}\) times the amplitude. Reason : In SHM, kinetic energy is zero when potential energy is maximum.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
\(E_{k}=\dfrac{1}{2} m \omega^{2}\left(A^{2}-x^{2}\right)\) \(U=\dfrac{1}{2} m \omega^{2} x^{2}\) When \(x=\dfrac{A}{\sqrt{2}}\), then \(E_{k}=U\) When \(x=0, U=U_{\text {min }}=0\) and \(E_{k}=\left(E_{k}\right)_{\max }=\dfrac{m \omega^{2} A^{2}}{2}\) So correct option is (2).
PHXI14:OSCILLATIONS
364088
A particle of mass \(1 \mathrm{~kg}\) is undergoing S.H.M., for which graph between force and displacement (from mean position) is shown. Its time period, in seconds, is:
1 \(\pi / 3\)
2 \(2 \pi / 3\)
3 \(\pi / 6\)
4 \(3 / \pi\)
Explanation:
\(F=-m \omega^{2} x\) so \(\omega^{2}=\dfrac{13.5}{1.5}=9\) \(\Rightarrow \omega=3\) \(\Rightarrow T=\dfrac{2 \pi}{3}\)
PHXI14:OSCILLATIONS
364089
The amplitude of a simple harmonic oscillator is doubled. Which of the following is doubled?
