364129
Assertion : A small body of mass \(0.1\;kg\) is undergoing SHM of amplitude \(1.0\;m\) and period \(0.2\;s\). The maximum value of the force acting on it is \(98.7\;N\). Reason : Maximum force acting on it cannot be found with data.
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:
Acceleration in SHM \(a=-\omega^{2} x\) \(\Rightarrow|F|=m \omega^{2} x\) \(=(0.1)\left(\dfrac{2 \pi}{0.2}\right)^{2}\) \( = 98.7\;N\) So correct option is (3).
PHXI14:OSCILLATIONS
364130
\(U\) is the \(P E\) of an oscillating particle and \(F\) is the force acting on it at a given instant. Which of the following is true?
1 \(\dfrac{U}{F}+x=0\)
2 \(\dfrac{2 U}{F}+x=0\)
3 \(\dfrac{F}{U}+=0\)
4 \(\dfrac{F}{2 U}+x=0\)
Explanation:
Potential energy, \(U=\dfrac{1}{2} K x^{2}\) \(\begin{aligned}& 2 U=k x^{2} \therefore F=-k x \\& 2 U=-F x \\& \dfrac{2 U}{F}=-x \\& \dfrac{2 U}{F}+x=0\end{aligned}\)
PHXI14:OSCILLATIONS
364131
A particle of mass \(m\) is executing SHM about the origin on \(x\)-axis with frequency \(\sqrt{\dfrac{k a}{\pi m}}\), where \(k\) is a constant and \(a\) is the amplitude. Find its potential energy, if \(x\) is the displacement at time \(t\).
1 \(k a^{2} x\)
2 \(ka{x^2}\)
3 \(2 \pi k x^{3}\)
4 \(2 \pi k a x^{2}\)
Explanation:
\(2 \pi f=\omega ; 2 \pi \sqrt{\dfrac{k a}{\pi m}}=\omega\) Potential energy \(U=\dfrac{1}{2} m \omega^{2} x=2 \pi k a x^{2}\)
PHXI14:OSCILLATIONS
364132
A particle of mass \(10\,gm\) is placed in a potential field given by \(V=\left(50 x^{2}+100\right) J / k g\). The frequency of oscillation in cycle/sec is:
364129
Assertion : A small body of mass \(0.1\;kg\) is undergoing SHM of amplitude \(1.0\;m\) and period \(0.2\;s\). The maximum value of the force acting on it is \(98.7\;N\). Reason : Maximum force acting on it cannot be found with data.
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:
Acceleration in SHM \(a=-\omega^{2} x\) \(\Rightarrow|F|=m \omega^{2} x\) \(=(0.1)\left(\dfrac{2 \pi}{0.2}\right)^{2}\) \( = 98.7\;N\) So correct option is (3).
PHXI14:OSCILLATIONS
364130
\(U\) is the \(P E\) of an oscillating particle and \(F\) is the force acting on it at a given instant. Which of the following is true?
1 \(\dfrac{U}{F}+x=0\)
2 \(\dfrac{2 U}{F}+x=0\)
3 \(\dfrac{F}{U}+=0\)
4 \(\dfrac{F}{2 U}+x=0\)
Explanation:
Potential energy, \(U=\dfrac{1}{2} K x^{2}\) \(\begin{aligned}& 2 U=k x^{2} \therefore F=-k x \\& 2 U=-F x \\& \dfrac{2 U}{F}=-x \\& \dfrac{2 U}{F}+x=0\end{aligned}\)
PHXI14:OSCILLATIONS
364131
A particle of mass \(m\) is executing SHM about the origin on \(x\)-axis with frequency \(\sqrt{\dfrac{k a}{\pi m}}\), where \(k\) is a constant and \(a\) is the amplitude. Find its potential energy, if \(x\) is the displacement at time \(t\).
1 \(k a^{2} x\)
2 \(ka{x^2}\)
3 \(2 \pi k x^{3}\)
4 \(2 \pi k a x^{2}\)
Explanation:
\(2 \pi f=\omega ; 2 \pi \sqrt{\dfrac{k a}{\pi m}}=\omega\) Potential energy \(U=\dfrac{1}{2} m \omega^{2} x=2 \pi k a x^{2}\)
PHXI14:OSCILLATIONS
364132
A particle of mass \(10\,gm\) is placed in a potential field given by \(V=\left(50 x^{2}+100\right) J / k g\). The frequency of oscillation in cycle/sec is:
364129
Assertion : A small body of mass \(0.1\;kg\) is undergoing SHM of amplitude \(1.0\;m\) and period \(0.2\;s\). The maximum value of the force acting on it is \(98.7\;N\). Reason : Maximum force acting on it cannot be found with data.
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:
Acceleration in SHM \(a=-\omega^{2} x\) \(\Rightarrow|F|=m \omega^{2} x\) \(=(0.1)\left(\dfrac{2 \pi}{0.2}\right)^{2}\) \( = 98.7\;N\) So correct option is (3).
PHXI14:OSCILLATIONS
364130
\(U\) is the \(P E\) of an oscillating particle and \(F\) is the force acting on it at a given instant. Which of the following is true?
1 \(\dfrac{U}{F}+x=0\)
2 \(\dfrac{2 U}{F}+x=0\)
3 \(\dfrac{F}{U}+=0\)
4 \(\dfrac{F}{2 U}+x=0\)
Explanation:
Potential energy, \(U=\dfrac{1}{2} K x^{2}\) \(\begin{aligned}& 2 U=k x^{2} \therefore F=-k x \\& 2 U=-F x \\& \dfrac{2 U}{F}=-x \\& \dfrac{2 U}{F}+x=0\end{aligned}\)
PHXI14:OSCILLATIONS
364131
A particle of mass \(m\) is executing SHM about the origin on \(x\)-axis with frequency \(\sqrt{\dfrac{k a}{\pi m}}\), where \(k\) is a constant and \(a\) is the amplitude. Find its potential energy, if \(x\) is the displacement at time \(t\).
1 \(k a^{2} x\)
2 \(ka{x^2}\)
3 \(2 \pi k x^{3}\)
4 \(2 \pi k a x^{2}\)
Explanation:
\(2 \pi f=\omega ; 2 \pi \sqrt{\dfrac{k a}{\pi m}}=\omega\) Potential energy \(U=\dfrac{1}{2} m \omega^{2} x=2 \pi k a x^{2}\)
PHXI14:OSCILLATIONS
364132
A particle of mass \(10\,gm\) is placed in a potential field given by \(V=\left(50 x^{2}+100\right) J / k g\). The frequency of oscillation in cycle/sec is:
364129
Assertion : A small body of mass \(0.1\;kg\) is undergoing SHM of amplitude \(1.0\;m\) and period \(0.2\;s\). The maximum value of the force acting on it is \(98.7\;N\). Reason : Maximum force acting on it cannot be found with data.
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:
Acceleration in SHM \(a=-\omega^{2} x\) \(\Rightarrow|F|=m \omega^{2} x\) \(=(0.1)\left(\dfrac{2 \pi}{0.2}\right)^{2}\) \( = 98.7\;N\) So correct option is (3).
PHXI14:OSCILLATIONS
364130
\(U\) is the \(P E\) of an oscillating particle and \(F\) is the force acting on it at a given instant. Which of the following is true?
1 \(\dfrac{U}{F}+x=0\)
2 \(\dfrac{2 U}{F}+x=0\)
3 \(\dfrac{F}{U}+=0\)
4 \(\dfrac{F}{2 U}+x=0\)
Explanation:
Potential energy, \(U=\dfrac{1}{2} K x^{2}\) \(\begin{aligned}& 2 U=k x^{2} \therefore F=-k x \\& 2 U=-F x \\& \dfrac{2 U}{F}=-x \\& \dfrac{2 U}{F}+x=0\end{aligned}\)
PHXI14:OSCILLATIONS
364131
A particle of mass \(m\) is executing SHM about the origin on \(x\)-axis with frequency \(\sqrt{\dfrac{k a}{\pi m}}\), where \(k\) is a constant and \(a\) is the amplitude. Find its potential energy, if \(x\) is the displacement at time \(t\).
1 \(k a^{2} x\)
2 \(ka{x^2}\)
3 \(2 \pi k x^{3}\)
4 \(2 \pi k a x^{2}\)
Explanation:
\(2 \pi f=\omega ; 2 \pi \sqrt{\dfrac{k a}{\pi m}}=\omega\) Potential energy \(U=\dfrac{1}{2} m \omega^{2} x=2 \pi k a x^{2}\)
PHXI14:OSCILLATIONS
364132
A particle of mass \(10\,gm\) is placed in a potential field given by \(V=\left(50 x^{2}+100\right) J / k g\). The frequency of oscillation in cycle/sec is:
