Tag: physics

Questions Related to physics

The ratio of intensities of two waves that produce interference pattern is 16:1, then the ratio of maximum and minimum intensities in the pattern is :

physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

  1. 25:9

  2. 9:25

  3. 1: 4

  4. 4:1

Show answer
Correct Option: A
Explanation:

Let the intensities of the two waves be $I _1$ and $I _2$.
Given :  $I _1:I _2 = 16:1$
Ratio of maximum and minimum intensities  $\dfrac{I _{max}}{I _{min}} = \bigg(\dfrac{\sqrt{I _1}  +\sqrt{I _2}}{\sqrt{I _1} - \sqrt{I _2}}\bigg)^2$
Or   $\dfrac{I _{max}}{I _{min}} = \bigg(\dfrac{\sqrt{\frac{I _1}{I _2}}  +1}{\sqrt{\frac{I _1}{I _2}} - 1}\bigg)^2$

Or  $\dfrac{I _{max}}{I _{min}} = \bigg(\dfrac{\sqrt{16}  +1}{\sqrt{16} - 1}\bigg)^2 = \bigg(\dfrac{4+1}{4-1}\bigg)^2$
$\implies  \ $  $\dfrac{I _{max}}{I _{min}} = \dfrac{25}{9}$

Consider the superposition of N harmonic waves of equal amplitude and frequency. If N is a very large number determine the resultant intensity in terms of the intensity $\left( { I } _{ 0 } \right)$ of each component wave for the condition when the component waves have identical phases.

physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

  1. ${ NI } _{ 0 }$

  2. ${ N }^{ 2 }{ I } _{ 0 }$

  3. $\sqrt { N } { I } _{ 0 }$

  4. ${ I } _{ 0 }$

Show answer
Correct Option: A
Explanation:

As all the waves are in phase and having same amplitude and frequency

So, the intensities will simply get add to give the resultant intensity
$\Rightarrow (Intensity) _{Resultant}=(I _0+I _0+.....I _0)-N\quad times\ \quad\quad\quad\quad\quad=NI _0$

Two waves having their intensities in the ratio 9:1 produce interference. In the interference pattern, the ratio of maximum to minimum intensity is equal to

physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

  1. 2:1

  2. 9:1

  3. 3:1

  4. 4:1

Show answer
Correct Option: D
Explanation:

Let the intensities of the two waves be $I _1$ and $I _2$.
Given :  $I _1:I _2 = 9:1$
Ratio of maximum and minimum intensities  $\dfrac{I _{max}}{I _{min}} = \bigg(\dfrac{\sqrt{I _1}  +\sqrt{I _2}}{\sqrt{I _1} - \sqrt{I _2}}\bigg)^2$
Or   $\dfrac{I _{max}}{I _{min}} = \bigg(\dfrac{\sqrt{\frac{I _1}{I _2}}  +1}{\sqrt{\frac{I _1}{I _2}} - 1}\bigg)^2$

Or  $\dfrac{I _{max}}{I _{min}} = \bigg(\dfrac{\sqrt{9}  +1}{\sqrt{9} - 1}\bigg)^2 = \bigg(\dfrac{3+1}{3-1}\bigg)^2$
$\implies  \ $  $\dfrac{I _{max}}{I _{min}} = \dfrac{16}{4} = \dfrac{4}{1}$

Assertion - Two sinusoidal waves on the same string exhibit interference.
Reason - these waves, add or cancel out according to the principle of superposition

physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

  2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

  3. Assertion is correct but Reason is incorrect

  4. Both Assertion and Reason are incorrect

Show answer
Correct Option: A
Explanation:

When there are two sinusoidal waves in a string, they cause interference of the waves. The principle of superposition is basic to the phenomenon of interference.

So, the assertion and reason both are correct and the reason is the correct explanation for the assertion.

Which of the following is true?

physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

  1. Both the light and sound waves exhibit interference

  2. Light waves exhibit interference

  3. Sound waves exhibit interference

  4. Neither sound waves nor light waves exhibit interference

Show answer
Correct Option: A

Work done by restoring force in a string within elastic limit is $-10\ J$. The maximum amount of heat produced in the string is :

elastic energy properties of material substances elasticity properties of matter physics

  1. $10\ J$

  2. $20\ J$

  3. $5\ J$

  4. $15\ J$

Show answer
Correct Option: A

If work done in stretching a wire by 1 mm is 2J. Then the work necessary for stretching another wire of same material but with double the radius and half the length by 1 mm in joule is

elastic energy properties of material substances elasticity properties of matter physics

  1. 1/4

  2. 4

  3. 8

  4. 16

Show answer
Correct Option: D
Explanation:

The stretching force $F=\dfrac{YA\Delta l}{l}$

where $Y=$Young's modulus, $A=$Area of cross-section of wire, $l=$actual length of wire, $\Delta l=$increase in length.
$F=\dfrac{Y\pi r^{2}\Delta l}{l}$
As the material is same $Y$ does not change.
$\dfrac{F _1}{F _2}=\dfrac{\dfrac{r _1^{2}\Delta l _1}{l _1}}{\dfrac{r _2^{2}\Delta l _2}{l _2}}$
Here $\Delta l _1=1mm$
$\Delta l _2=1mm$
$l _2=\dfrac{1}{2}l _1$
$r _2=2r _1$
$\dfrac{F _1}{F _2}=\dfrac{\dfrac{r _1^{2}\times 1mm}{l _1}}{\dfrac{4r _1^{2}\times 1mm}{\dfrac{1}{2}l _1}}$
$\dfrac{F _1}{F _2}=\dfrac{1}{8}$
The work done in stretching wire by amount $\Delta l$ is $W=\dfrac{1}{2} F\Delta l$
Hence $\dfrac{W _1}{W _2}=\dfrac{F _1}{F _2}=\dfrac{1}{8}$
As $F _1=2$
$F _2=2\times 8=16$
Hence the correct option is (D).

When a body mass $M$ is attached to power end of a wire (of length $L$) whose upper end is fixed, then the elongation of the wire is $l$. In this situation mark out the correct statement(s).

elastic energy properties of material substances elasticity properties of matter physics

  1. Loss in gravitational potential energy of $M$ is $Mgl$.

  2. Elastic potential energy stored in the wire is $\dfrac {Mgl}{2}$

  3. Elastic potential energy stored in the wire is $Mgl$

  4. Elastic potential energy stored in the wire is $\dfrac {Mgl}{3}$

Show answer
Correct Option: A,B
Explanation:

Since it moves $l$ distance against gravity, so gravitational potential energy=Mgl
Elastic potential energy=$1/2\times Stress\times Strain\times Volume=1/2\times \dfrac{Mg}{A} \times \dfrac{l}{L}\times AL=\dfrac{Mgl}{2}$

Match the columns

A B
(1) Speed of light (a) 4.3 light years away from earth
(2) Light year                (b) 300,000 km/s
(3) Sun (c) Nearest star
(4) Alpha Centauri (d) distance travelled by light in one year
(e) 18 light minutes away from the Earth
physics life cycle of stars evolution and end stages of stars the stars stars

  1. 1-d 2-d, 3-a, 4-e

  2. 1-a, 2-b, 3-c, 4-e

  3. 1-d, 2-b, 3-e, 4-c

  4. 1-b, 2-d, 3-c, 4-a

Show answer
Correct Option: D
Explanation:

The speed of light is 300,000 km/s.
Light year is the distance travelled by light in one year.
Sun is the nearest star from Earth.
Alpha Centauri is 4.3 light years away from Earth.

The observed wavelength of light coming from a distant galaxy is found to be increased by $0.5\%$ as compared with that coming from a terrestrial source. The galaxy is.

physics life cycle of stars evolution and end stages of stars the stars stars

  1. Stationary with respect t to the earth

  2. Approching the earth with velocity of light

  3. Receding from the earth with velocity of light

  4. Receding from the earth with a velocity equal to $1.5\times 10^{6}m/s$

Show answer
Correct Option: D
Explanation:

$\displaystyle\frac{\Delta \lambda}{\lambda}=\frac{v}{c}$
Now, $\Delta\lambda=\displaystyle\frac{0.5}{100} \lambda$
$\Rightarrow \displaystyle\frac{\Delta\lambda}{\lambda}=\frac{0.5}{100}$
$\therefore v=\displaystyle\frac{0.5}{100}\times c=\frac{0.5}{100}\times 3\times 10^8$
$=1.5\times 10^6m/s$
increase in $\lambda$ indicates that the star is receding.