Tag: a few applications of linear shm

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

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

  1. $20s$
  2. $50s$
  3. $40s$
  4. $5s$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
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,

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

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

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

  1. 4πG/3gR

  2. 3πR/4gG

  3. 3g/4πRG

  4. πRg/12G
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $g=\cfrac{GM}{R^2}\P=\cfrac{3g}{4\pi RG}$

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

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

  1. Be less

  2. Be more

  3. Remain unchanged

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
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. 

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

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

  1. losses $764 \ s$
  2. losses $924 \ s$
  3. gains $236 \ s$
  4. losses $864 \ s$
  5. gains $346 \ s$
Reveal answer Fill a bubble to check yourself
D Correct answer
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$=(0.01\times24\times3600)seconds\=864seconds$

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

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

  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. $\dfrac{d^2 x}{dt^2} + \pi^2 x = 0$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The differential equation for simple harmonic motion is d^2x/dt^2 + omega^2 x = 0. For a seconds pendulum, the time period T = 2 seconds, so angular frequency omega = 2pi/T = 2pi/2 = pi. Substituting omega^2 into the equation gives d^2x/dt^2 + pi^2 x = 0.

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

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 

  1. $3\sqrt { 3 } mg$
  2. $\frac { 1 }{ 2 } mg(2\sqrt { 3 } -1)$
  3. $\frac { 1 }{ 2 } mg(3\sqrt { 3 } +2)$
  4. $\frac { 1 }{ 2 } mg(3-\sqrt { 2 } )$
Reveal answer Fill a bubble to check yourself
B Correct answer