364347
The motion which is not simple harmonic is:
1 Motion of simple pendulum
2 Vertical oscillation of a spring
3 Vertical oscialltion of a wooden plank floating in a liquid
4 Motion of a planet around the sun
Explanation:
The motion of planets around the sun is periodic but not simple harmonic motion.
PHXI14:OSCILLATIONS
364348
A round metal hoop is suspended on the edge by a hook. The hoop can oscillate side to side in the plane of the hoop, or it can oscillate back and fourth in a direction perpendicular to the plane of the hoop. For which mode will the frequency of oscillation be larger?
1 The frequency of oscillation will be the same in either mode
2 Oscillations in the plane of the hoop
3 Oscillations perpendicular to the plane of the hoop
4 None of these
Explanation:
\(T = 2\pi \sqrt {\frac{I}{{mgR}}} \) For side by side oscillations \(I_{1}=2 m R^{2}\) (Passing the centre and plane) \(I_{2}=\dfrac{m R^{2}}{2}(\) Passing through edge \()\) As \(I_{1}>I_{2} \Rightarrow T_{1}>T_{2} \Rightarrow f_{1} < f_{2}\)
PHXI14:OSCILLATIONS
364349
A wooden cube (density of wood '\(d\)') of side ' \(l\) ' floats in a liquid of density '\(\rho\)' with its upper and lower surface horizontal. If the cube is pushed slightly down and relased, it performs simple harmonic motion of period '\(T\)' to
1 \(2 \pi \sqrt{\dfrac{l d}{\rho g}}\)
2 \(2 \pi \sqrt{\dfrac{l \rho}{d g}}\)
3 \(2 \pi \sqrt{\dfrac{l d}{(\rho-d) g}}\)
4 \(2 \pi \sqrt{\dfrac{l \rho}{(\rho-d) g}}\)
Explanation:
At equilibrium \(F_{b}=m g\) \(\rho A l_{0} g=d l g\) Restoring force, \(\begin{aligned}& F_{r}=m g-F_{b}^{\prime} \\& F=m g-\rho A\left(l_{0}+x\right) g \\& d A l a=d A l g-\rho A l_{0} g-\rho g A x \\& a=-\dfrac{\rho g}{d l} x\end{aligned}\) Therefore, wooden cube performs S.H.M. \(\therefore \omega=\sqrt{\dfrac{\rho g}{d l}} \Rightarrow T=2 \pi \sqrt{\dfrac{l d}{\rho g}}\)
PHXI14:OSCILLATIONS
364350
Two oscillating systems; a simple pendulum and a vertical spring-mass-system have same time period of motion on the surface of the Earth. If both are taken to the moon, then-
1 Time period of the simple pendulum will be more than that of the spring-mass system.
2 Time period of the simple pendulum will be equal is that is of the spring-mass system.
3 Time period of the simple pendulum will be less than of the spring-mass system.
4 Nothing can be said definitely without observation.
Explanation:
For simple pendulum: \(T = 2\pi \sqrt {\frac{\ell }{g}} \) As \(g\) will decrease on moon, time period will increase For spring mass system : \(T = 2\pi \sqrt {\frac{m}{k}} \) It will not change and remains the same
364347
The motion which is not simple harmonic is:
1 Motion of simple pendulum
2 Vertical oscillation of a spring
3 Vertical oscialltion of a wooden plank floating in a liquid
4 Motion of a planet around the sun
Explanation:
The motion of planets around the sun is periodic but not simple harmonic motion.
PHXI14:OSCILLATIONS
364348
A round metal hoop is suspended on the edge by a hook. The hoop can oscillate side to side in the plane of the hoop, or it can oscillate back and fourth in a direction perpendicular to the plane of the hoop. For which mode will the frequency of oscillation be larger?
1 The frequency of oscillation will be the same in either mode
2 Oscillations in the plane of the hoop
3 Oscillations perpendicular to the plane of the hoop
4 None of these
Explanation:
\(T = 2\pi \sqrt {\frac{I}{{mgR}}} \) For side by side oscillations \(I_{1}=2 m R^{2}\) (Passing the centre and plane) \(I_{2}=\dfrac{m R^{2}}{2}(\) Passing through edge \()\) As \(I_{1}>I_{2} \Rightarrow T_{1}>T_{2} \Rightarrow f_{1} < f_{2}\)
PHXI14:OSCILLATIONS
364349
A wooden cube (density of wood '\(d\)') of side ' \(l\) ' floats in a liquid of density '\(\rho\)' with its upper and lower surface horizontal. If the cube is pushed slightly down and relased, it performs simple harmonic motion of period '\(T\)' to
1 \(2 \pi \sqrt{\dfrac{l d}{\rho g}}\)
2 \(2 \pi \sqrt{\dfrac{l \rho}{d g}}\)
3 \(2 \pi \sqrt{\dfrac{l d}{(\rho-d) g}}\)
4 \(2 \pi \sqrt{\dfrac{l \rho}{(\rho-d) g}}\)
Explanation:
At equilibrium \(F_{b}=m g\) \(\rho A l_{0} g=d l g\) Restoring force, \(\begin{aligned}& F_{r}=m g-F_{b}^{\prime} \\& F=m g-\rho A\left(l_{0}+x\right) g \\& d A l a=d A l g-\rho A l_{0} g-\rho g A x \\& a=-\dfrac{\rho g}{d l} x\end{aligned}\) Therefore, wooden cube performs S.H.M. \(\therefore \omega=\sqrt{\dfrac{\rho g}{d l}} \Rightarrow T=2 \pi \sqrt{\dfrac{l d}{\rho g}}\)
PHXI14:OSCILLATIONS
364350
Two oscillating systems; a simple pendulum and a vertical spring-mass-system have same time period of motion on the surface of the Earth. If both are taken to the moon, then-
1 Time period of the simple pendulum will be more than that of the spring-mass system.
2 Time period of the simple pendulum will be equal is that is of the spring-mass system.
3 Time period of the simple pendulum will be less than of the spring-mass system.
4 Nothing can be said definitely without observation.
Explanation:
For simple pendulum: \(T = 2\pi \sqrt {\frac{\ell }{g}} \) As \(g\) will decrease on moon, time period will increase For spring mass system : \(T = 2\pi \sqrt {\frac{m}{k}} \) It will not change and remains the same
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PHXI14:OSCILLATIONS
364347
The motion which is not simple harmonic is:
1 Motion of simple pendulum
2 Vertical oscillation of a spring
3 Vertical oscialltion of a wooden plank floating in a liquid
4 Motion of a planet around the sun
Explanation:
The motion of planets around the sun is periodic but not simple harmonic motion.
PHXI14:OSCILLATIONS
364348
A round metal hoop is suspended on the edge by a hook. The hoop can oscillate side to side in the plane of the hoop, or it can oscillate back and fourth in a direction perpendicular to the plane of the hoop. For which mode will the frequency of oscillation be larger?
1 The frequency of oscillation will be the same in either mode
2 Oscillations in the plane of the hoop
3 Oscillations perpendicular to the plane of the hoop
4 None of these
Explanation:
\(T = 2\pi \sqrt {\frac{I}{{mgR}}} \) For side by side oscillations \(I_{1}=2 m R^{2}\) (Passing the centre and plane) \(I_{2}=\dfrac{m R^{2}}{2}(\) Passing through edge \()\) As \(I_{1}>I_{2} \Rightarrow T_{1}>T_{2} \Rightarrow f_{1} < f_{2}\)
PHXI14:OSCILLATIONS
364349
A wooden cube (density of wood '\(d\)') of side ' \(l\) ' floats in a liquid of density '\(\rho\)' with its upper and lower surface horizontal. If the cube is pushed slightly down and relased, it performs simple harmonic motion of period '\(T\)' to
1 \(2 \pi \sqrt{\dfrac{l d}{\rho g}}\)
2 \(2 \pi \sqrt{\dfrac{l \rho}{d g}}\)
3 \(2 \pi \sqrt{\dfrac{l d}{(\rho-d) g}}\)
4 \(2 \pi \sqrt{\dfrac{l \rho}{(\rho-d) g}}\)
Explanation:
At equilibrium \(F_{b}=m g\) \(\rho A l_{0} g=d l g\) Restoring force, \(\begin{aligned}& F_{r}=m g-F_{b}^{\prime} \\& F=m g-\rho A\left(l_{0}+x\right) g \\& d A l a=d A l g-\rho A l_{0} g-\rho g A x \\& a=-\dfrac{\rho g}{d l} x\end{aligned}\) Therefore, wooden cube performs S.H.M. \(\therefore \omega=\sqrt{\dfrac{\rho g}{d l}} \Rightarrow T=2 \pi \sqrt{\dfrac{l d}{\rho g}}\)
PHXI14:OSCILLATIONS
364350
Two oscillating systems; a simple pendulum and a vertical spring-mass-system have same time period of motion on the surface of the Earth. If both are taken to the moon, then-
1 Time period of the simple pendulum will be more than that of the spring-mass system.
2 Time period of the simple pendulum will be equal is that is of the spring-mass system.
3 Time period of the simple pendulum will be less than of the spring-mass system.
4 Nothing can be said definitely without observation.
Explanation:
For simple pendulum: \(T = 2\pi \sqrt {\frac{\ell }{g}} \) As \(g\) will decrease on moon, time period will increase For spring mass system : \(T = 2\pi \sqrt {\frac{m}{k}} \) It will not change and remains the same
364347
The motion which is not simple harmonic is:
1 Motion of simple pendulum
2 Vertical oscillation of a spring
3 Vertical oscialltion of a wooden plank floating in a liquid
4 Motion of a planet around the sun
Explanation:
The motion of planets around the sun is periodic but not simple harmonic motion.
PHXI14:OSCILLATIONS
364348
A round metal hoop is suspended on the edge by a hook. The hoop can oscillate side to side in the plane of the hoop, or it can oscillate back and fourth in a direction perpendicular to the plane of the hoop. For which mode will the frequency of oscillation be larger?
1 The frequency of oscillation will be the same in either mode
2 Oscillations in the plane of the hoop
3 Oscillations perpendicular to the plane of the hoop
4 None of these
Explanation:
\(T = 2\pi \sqrt {\frac{I}{{mgR}}} \) For side by side oscillations \(I_{1}=2 m R^{2}\) (Passing the centre and plane) \(I_{2}=\dfrac{m R^{2}}{2}(\) Passing through edge \()\) As \(I_{1}>I_{2} \Rightarrow T_{1}>T_{2} \Rightarrow f_{1} < f_{2}\)
PHXI14:OSCILLATIONS
364349
A wooden cube (density of wood '\(d\)') of side ' \(l\) ' floats in a liquid of density '\(\rho\)' with its upper and lower surface horizontal. If the cube is pushed slightly down and relased, it performs simple harmonic motion of period '\(T\)' to
1 \(2 \pi \sqrt{\dfrac{l d}{\rho g}}\)
2 \(2 \pi \sqrt{\dfrac{l \rho}{d g}}\)
3 \(2 \pi \sqrt{\dfrac{l d}{(\rho-d) g}}\)
4 \(2 \pi \sqrt{\dfrac{l \rho}{(\rho-d) g}}\)
Explanation:
At equilibrium \(F_{b}=m g\) \(\rho A l_{0} g=d l g\) Restoring force, \(\begin{aligned}& F_{r}=m g-F_{b}^{\prime} \\& F=m g-\rho A\left(l_{0}+x\right) g \\& d A l a=d A l g-\rho A l_{0} g-\rho g A x \\& a=-\dfrac{\rho g}{d l} x\end{aligned}\) Therefore, wooden cube performs S.H.M. \(\therefore \omega=\sqrt{\dfrac{\rho g}{d l}} \Rightarrow T=2 \pi \sqrt{\dfrac{l d}{\rho g}}\)
PHXI14:OSCILLATIONS
364350
Two oscillating systems; a simple pendulum and a vertical spring-mass-system have same time period of motion on the surface of the Earth. If both are taken to the moon, then-
1 Time period of the simple pendulum will be more than that of the spring-mass system.
2 Time period of the simple pendulum will be equal is that is of the spring-mass system.
3 Time period of the simple pendulum will be less than of the spring-mass system.
4 Nothing can be said definitely without observation.
Explanation:
For simple pendulum: \(T = 2\pi \sqrt {\frac{\ell }{g}} \) As \(g\) will decrease on moon, time period will increase For spring mass system : \(T = 2\pi \sqrt {\frac{m}{k}} \) It will not change and remains the same