Tag: physics

Questions Related to physics

A sphere of radius r is kept on a concave mirror of radius of curvature R. The arrangement is kept on a horizontal table (the surface of concave mirror is frictionless and sliding not rolling). If the sphere is displaced from its equilibrium position and left, then it executes S.H.M. The period of oscillation will be  

physics free, damped and forced oscillations forced vibration forced vibrations free, forced and damped oscillations

  1. $\pi \times { \left( \dfrac { (R-r)1.4 }{ g } \right) } $

  2. $2\pi \times  { \left( \dfrac { R-r }{ g } \right) } $

  3. $\sqrt [ 2\pi ]{ \left( \dfrac { r\quad R }{ g } \right) } $

  4. ${ \left( \dfrac { R }{ g\quad r } \right) } $

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Correct Option: B

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5 s .In another 10 s it will decrease to $\alpha $ times its original magnitude where $\alpha $ equals :  

physics free, damped and forced oscillations forced vibration forced vibrations free, forced and damped oscillations

  1. 0.7

  2. 0.81

  3. 0.729

  4. 0.6

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Correct Option: C

Three infinitely long thin wires, each carrying current I in the same direction, are in the $x-y$ plane of a gravity free space. The central wire is along the y-axis while the other two are along $x=\pm\ d$.
(a) Find the locus of the points for which the magnetic field $B$ is zero.
(b) If the central wire is displaced along the z-direction by a small amount and released, show that it will execute simple harmonic motion. If the linear density of the wires is $\lambda$, find the frequency of oscillation.

physics free, damped and forced oscillations forced vibration forced vibrations free, forced and damped oscillations

  1. $\dfrac{1}{4\pi}\sqrt{\dfrac{\mu _oI^2}{\pi\lambda d^2}}$.

  2. $\dfrac{1}{2\pi}\sqrt{\dfrac{\mu _oI^2}{\pi\lambda d^2}}$.

  3. $\dfrac{2}{2\pi}\sqrt{\dfrac{\mu _oI^2}{\pi\lambda d^2}}$.

  4. $\dfrac{3}{2\pi}\sqrt{\dfrac{\mu _oI^2}{\pi\lambda d^2}}$.

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Correct Option: B

A student performs an experiment for determination of $\Bigg \lgroup g = \frac{4\pi^2 l}{T^2} \Bigg \rgroup$, l = 1m, and he commits an error of $\Delta l$ For T he takes the time of n oscillations with the stop watch of least count $\Delta T$ and he commits a human error of 0.1 s. For which of the following data, the measurement of g will be most accurate?

physics free, damped and forced oscillations forced vibration forced vibrations free, forced and damped oscillations

  1. $\Delta L = 0.5, \ \Delta T = 0.1 , \ n = 20$

  2. $\Delta L = 0.5, \ \Delta T = 0.1 , \ n = 50$

  3. $\Delta L = 0.5, \ \Delta T = 0.01 , \ n = 20$

  4. $\Delta L = 0.5, \ \Delta T = 0.05 , \ n = 50$

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Correct Option: B
Explanation:

It is given that $g$ is determined by $:g = \frac{{4{\pi ^2}l}}{{{T^2}}}$

Taking log and differentiating$,$
$ \Rightarrow \frac{{\Delta g}}{g} = \frac{{\Delta l}}{l} + \frac{{2\Delta T}}{T}$ 
Now$,$ $g$ is most accurate in the case in which error in $g\left( {l.e\,\Delta g} \right)$ is minimum$.$ In case $B,$ number of repetitions to perform the experiment is maximum and ${\Delta g}$  is minimum$.$
Hence,
option $(B)$ is correct answer.

A particle moves such that its acceleration is given by : $\alpha=-\beta(x-2)$
Here :$\beta$ is a positive constant and x the position from oigin. Time period of oscillations is:

physics free, damped and forced oscillations forced vibration forced vibrations free, forced and damped oscillations

  1. $2\pi+\sqrt\beta$

  2. $2\pi +\sqrt { \cfrac { 1 }{ \beta } } $

  3. $2\pi+\sqrt{\beta+2}$

  4. $2\pi +\sqrt { \cfrac { 1 }{ \beta +2} } $

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Correct Option: B

A simple pendulum suspended from the ceiling of a stationary trolley has a length $l$ its period of oscillation is $2\pi\sqrt{l/g}$. Whqat will be its period of oscillation if the trolley moves forward with an acceleration $f$?

physics free, damped and forced oscillations forced vibration forced vibrations free, forced and damped oscillations

  1. g

  2. l

  3. d

  4. m

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Correct Option: A

Find the time period of small oscillations of the following systems. 

physics free, damped and forced oscillations forced vibration forced vibrations free, forced and damped oscillations

  1. A metre stick suspended through the 20 cm mark.

  2. A ring of mass m and radius r suspended through a point on its perphery.

  3. A uniform square plate of edge a suspended through a corner.

  4. A uniform disc of mass m and radius r suspended through a point r/2 away from the centre.

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Correct Option: A

A uniform circular disc of radius $R$ oscillates about a horizontal axis in its own plane. The distance of the axis from the center for the period of oscillation is maximum, will be :

physics free, damped and forced oscillations forced vibration forced vibrations free, forced and damped oscillations

  1. $R$

  2. $\dfrac{R}{\sqrt 2}$

  3. $\dfrac{R}{3}$

  4. $\dfrac{R}{4}$

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Correct Option: B

Find the frequency of oscillation of the spheres

physics free, damped and forced oscillations forced vibration forced vibrations free, forced and damped oscillations

  1. $\frac{1}{{2\pi }}\sqrt {\dfrac{{35K}}{{46m}}} $

  2. $\frac{1}{{2\pi }}\sqrt {\dfrac{{46K}}{{35m}}} $

  3. $\frac{1}{{2\pi }}\sqrt {\dfrac{{25K}}{{46m}}} $

  4. $\frac{1}{{2\pi }}\sqrt {\dfrac{{21K}}{{46m}}} $

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Correct Option: A

Find the frequency of oscillation of the spheres

physics free, damped and forced oscillations forced vibration forced vibrations free, forced and damped oscillations

  1. $ \dfrac { 1 }{ 2\pi } \sqrt { \dfrac { 35K }{ 46m } } $

  2. $ \dfrac { 1 }{ 2\pi } \sqrt { \dfrac { 46K }{ 35m } } $

  3. $ \dfrac { 1 }{ 2\pi } \sqrt { \dfrac { 25K }{ 46m } } $

  4. $ \dfrac { 1 }{ 2\pi } \sqrt { \dfrac {21K }{ 46m } } $

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Correct Option: C