Tag: a few applications of linear shm

Questions Related to a few applications of linear shm

The frequency of a seconds pendulum is equal to :

physics measurements and experimentation a few applications of linear shm simple pendulum example of simple harmonic motion

  1. 0.5 Hz

  2. 1 Hz

  3. 2 Hz

  4. 0.1 Hz

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Correct Option: A
Explanation:

The frequency of seconds pendulum is $= \dfrac{1}{2} = 0.5$ HZ

The time taken to complete $20$ oscillations by a seconds pendulum is: 

physics measurements and experimentation a few applications of linear shm simple pendulum example of simple harmonic motion

  1. $20s$

  2. $50s$

  3. $40s$

  4. $5s$

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Correct Option: C
Explanation:

We know that the time period of a seconds pendulum is $T=2$ sec. One second for a swing in one direction and one second for the return swing. 

Thus, time taken to complete one oscillation is $2$ sec.
Hence, time taken to complete 20 oscillations is $2\times 20=40$ sec.

The length of a second's pendulum on the surface of the earth is equal to 99.49 cm. True or false.

physics measurements and experimentation a few applications of linear shm simple pendulum example of simple harmonic motion

  1. True

  2. False

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Correct Option: A
Explanation:

The time period of seconds pendulum T = 2 seconds, acceleration due to gravity at earth g= 980 $\dfrac { cm }{ { s }^{ 2 } } $,It '$l$' is the length of pendulum,

$l=\dfrac { { T }^{ 2 }g }{ 4{ \pi  }^{ 2 } } \ \Rightarrow l=\dfrac { 4\times 980 }{ 4\times \left( \dfrac { 22 }{ 7 }  \right) ^{ 2 } } =\dfrac { 4\times 980\times 49 }{ 4\times 489 } =99.49$

If R is the radius of the earth and g the acceleration due to gravity on the earth's surface, the mean density of the earth is

physics measurements and experimentation a few applications of linear shm simple pendulum example of simple harmonic motion

  1. 4πG/3gR

  2. 3πR/4gG

  3. 3g/4πRG     

  4. πRg/12G

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Correct Option: C
Explanation:

We know that

$g=\cfrac{GM}{R^2}$
Also, density $=mass\times volume$
$M=density\times volume\M=P\times\cfrac{4\pi R^3}{3R^2}=P\times\cfrac{4\pi R}{3}$
Put value of m in $g=\cfrac{GM}{R^2}\P=\cfrac{3g}{4\pi RG}$

Let the time period of a seconds pendulum is $2.5\ s.$ Tell by how much time will the clock behind in $10\ hrs.$

physics measurements and experimentation a few applications of linear shm simple pendulum example of simple harmonic motion

  1. $2.5\ hr$

  2. $2\ hr$

  3. $1.5\ hr$

  4. $None$

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Correct Option: C

The mass of a bob, suspended in a simple pendulum, is halved from the initial mass, its time period will :

physics measurements and experimentation a few applications of linear shm simple pendulum example of simple harmonic motion

  1. Be less

  2. Be more

  3. Remain unchanged

  4. None of these

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Correct Option: C
Explanation:

The time period of simple pendulum id given by

$T=2\pi \sqrt{\dfrac{l}{g}}$
where, $l=$ length of simple pendulum
$g=$ acceleration due to gravity
$T=$ Time period
The time period of simple pendulum is independent of the mass of bob, the time period remains unchanged,when mass of bob will change.
The correct option is C. 

If the length of a seconds pendulum is increased by $2$% then what is loss and gain in a day?

physics measurements and experimentation a few applications of linear shm simple pendulum example of simple harmonic motion

  1. losses $764 \ s$

  2. losses $924 \ s$

  3. gains $236 \ s$

  4. losses $864 \ s$

  5. gains $346 \ s$

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Correct Option: D
Explanation:

$T _0=2\pi\sqrt{\cfrac{l}{g}}\T^1=2\pi\sqrt{\cfrac{l+l\times2/100}{g}}\ \cfrac{T _0}{T^1}=\cfrac{\sqrt{100}}{\sqrt{102}}\ T^1=\cfrac{\sqrt{102}}{\sqrt{100}}T _0\T^1=1.0099T _0\approx  1.01T _0\Loss=(1.01-1)T _0=0.01T _0$

In one second, it looses $0.01sec$
$\Rightarrow$ Total time loose in one day$=(0.01\times24\times3600)seconds\=864seconds$

If the length of second's pendulum is increased by $2\%$, how many second will it lose per day?

physics measurements and experimentation a few applications of linear shm simple pendulum example of simple harmonic motion

  1. $923$ s

  2. $3727$ s

  3. $3642$ s

  4. $864$ s

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Correct Option: D

The different equation of simple harmonic motion for a seconds pendulum is:

physics measurements and experimentation a few applications of linear shm simple pendulum example of simple harmonic motion

  1. $\dfrac{d^2 x}{dt^2} + x = 0$

  2. $\dfrac{d^2 x}{dt^2} + \pi x = 0$

  3. $\dfrac{d^2 x}{dt^2} + 4 \pi x = 0$

  4. $\dfrac{d^2 x}{dt^2} + \pi^2 x = 0$

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Correct Option: A

A simple pendulum with a bob of mass m swings with an angular amplitude of ${ 60 }^{ 0 }$, when its angular displacement is ${ 30 }^{ 0 }$, the tension of string would be 

physics measurements and experimentation a few applications of linear shm simple pendulum example of simple harmonic motion

  1. $3\sqrt { 3 } mg$

  2. $\frac { 1 }{ 2 } mg(2\sqrt { 3 } -1)$

  3. $\frac { 1 }{ 2 } mg(3\sqrt { 3 } +2)$

  4. $\frac { 1 }{ 2 } mg(3-\sqrt { 2 } )$

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Correct Option: B