Tag: physics

Questions Related to physics

A person observe two points on a string as a travelling wave passes them. The points are at $x _ { 1 } = 0$ and $x _ { 2 } = 1 m.$ The transverse motions of the two points are found to be as follows:
$y _ { 1 } = 0.2 \sin 3 \pi t$
$y _ { 2 } = 0.2 \sin ( 3 \pi t + \pi/8 )$
What is the maximum wavelength?

  1. $32 m$

  2. $16 m$

  3. $8 m$

  4. $4 m$


Correct Option: B

A string of length $L$ is stretched along the $x-axis$ and is rigidly clamped at its two ends. It undergoes transverse vibration. If $n$ is an integer, which of the following relations may represent the shape of the string at any time:-

  1. $y = A \sin \left( \dfrac { n \pi x } { L } \right) \cos \omega t$

  2. $y = A \sin \left( \dfrac { n \pi x } { L } \right) \sin \omega t $

  3. $y = A \cos \left( \dfrac { n \pi x } { L } \right) \cos \omega t $

  4. $y = A \cos \left( \dfrac { \operatorname { n\pi } x } { L } \right) \sin \omega t$


Correct Option: B

String $B$ has twice the length, twice the diameter, twice the tension and twice the density of string $A$. The overtone of $B$ that will be in unison with fundamental frequency of $A$ is 

  1. $1st$

  2. $2nd$

  3. $3rd$

  4. $4th$


Correct Option: B

A particle starting from mean position having equation $y=A\sin { \pi t } $ .Find velocity of particle at t=1/3 sec.

  1. $\dfrac { A\pi }{ 2 } $

  2. $\dfrac { \sqrt { 3 } }{ 2 } A\pi $

  3. $A\pi $

  4. zero


Correct Option: C

Two strings of same material are stretched to the same tension. If their radii are in the ratio $1:2$, then respective wave velocities in them will be in ratio

  1. $4:1$

  2. $2:1$

  3. $1:2$

  4. $1:4$


Correct Option: B
Explanation:
We know that the velocity of wave in a stretched string is given by:
$v=\sqrt{\dfrac{TL}{m}}$
Where $T=$tension$=$same for both
$L=$length$=$same for both
$m=$mass
hence
$v\propto \dfrac{1}{\sqrt{m}}$
we know that
mass$=$volume$\times$ density
$=\pi r^2L\rho$
Since L and $\rho$ are equal for both the strings, hence $m\propto r^2$
$\Rightarrow v\propto \dfrac{1}{\sqrt{m}}\propto \dfrac{1}{r}$
$\Rightarrow \dfrac{v _1}{v _2}=\dfrac{r _2}{r _1}=2:1$.

The equation of a ware is represented by $y = {10^4}\,\sin \,\left[ {100t - \frac{X}{{10}}} \right]$ here $X$ in meter and $t$ in second$.$ The velocity of the wave will be $:-$

  1. $100 m/s$

  2. $250 m/s$

  3. $750 m/s$

  4. $1000 m/s$


Correct Option: D

A stretched string is $1\ m$ long. Its liner density is $0.5\ gm/m$. It is stretched with a force of $20\ N$. If plucked at a distance of $25\ cm$ from one end, the frequency of the tone emitted by it is

  1. $100\ Hz$

  2. $200\ Hz$

  3. $300\ Hz$

  4. $400\ Hz$


Correct Option: B

A particle moves with simple harmonic motion in a straight line. In first $\tau s,$, after starting from rest it travels a distance $a$, and in next $\tau s$ it travels $2a$, in same direction, then:

  1. amplitude of motion is $4a$

  2. time period of oscillations is $6$,

  3. amplitude of motion is $3a$$\tau $

  4. time period of oscillations is $8$,$\tau $


Correct Option: A

An elastic string carrying a baby of mass 'm' extends by 'e' . The body rotates in a vertical circle with critical velocity. The externsion in the string at the lowest position is 

  1. $2e$

  2. $4e$

  3. $6e$

  4. $8e$


Correct Option: C

The equation of a progressive wave for a wire is: 
$Y=4\sin{\left[\cfrac{\pi}{2}\left(8t-\cfrac{x}{8}\right)\right]}$. If $x$ and $y$ are measured in cm then velocity of wave is :

  1. $64 cm/s$ along $-x$ direction

  2. $32 cm/s$ along $-x$ direction

  3. $32 cm/s$ along $+x$ direction

  4. $64 cm/s$ along $+x$ direction


Correct Option: D
Explanation:

$\begin{array}{l} w=4\pi  \ K=\dfrac { \pi  }{ { 16 } }  \ v=\dfrac { w }{ K } =64\, m/s\, along\, \, +x-axis \ Hence, \ option\, \, D\, \, is\, correct\, \, answer. \end{array}$