Tag: simple pendulum

Questions Related to simple pendulum

The simple pendulum acts as second's pendulum on earth. Its time on a planet, whose mass and diameter are twice that of earth is:

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

  1. $\sqrt { 2 } s$

  2. $2\sqrt { 2 } s$

  3. $2s$

  4. $\dfrac { 1 }{ \sqrt { 2 } } s$

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Correct Option: B
Explanation:

Time period of second's pendulum is two second.
Second's pendulum is that simple pendulum whose time period of vibration is two seconds. The bob of such pendulum while oscillating passes through the mean position after every one second.
Noe,
Time period of simple pendulum is given by
$T=2\pi \sqrt { \left( \dfrac { l }{ g }  \right)  } $
or  $T\propto \dfrac { 1 }{ \sqrt { g }  } $             ......(i)
but  $g=\dfrac { GM }{ { R }^{ 2 } } $      (on earth)
and  ${ g }^{ \prime  }=\dfrac { G\left( 2M \right)  }{ 4{ R }^{ 2 } } $     (on planet)
$=\dfrac { 1 }{ 2 } \dfrac { GM }{ { R }^{ 2 } } =\dfrac { g }{ 2 } $
Equation (i) gives
$\dfrac { { T }^{ \prime  } }{ T } =\dfrac { \sqrt { g }  }{ \sqrt { { g }^{ \prime  } }  } =\sqrt { 2 } $
or  ${ T }^{ \prime  }=\sqrt { 2 } T$
  $=\sqrt { 2 } \times 2              \left( T=2s \right) $
  $=2\sqrt { 2 } s$

The length of a second's pendulum at a place where g = 9.8m/s $\displaystyle ^{2}$ is 90.2 cm. State whether 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: B
Explanation:

Time period of pendulum is:

$T =2\pi \sqrt [  ]{ \cfrac { l }{ g }  } $
$l=\cfrac { T^{ 2 }g }{ 4\pi ^{ 2 } } $
$l=\cfrac { 4\times 9.8 }{ 4\times \pi ^{ 2 } } $
$l=0.993m=99.3m$
$l$= length of pendulum 
$g$= $9.8m/s$
$T$ = Time period of seconds pendulum $=2s$
So, our given statement is false.

A second's pendulum can be used as a timing device

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 second's pendulum has a definite time period of 2 seconds. We can calculate the time by counting its no.of oscillation. So, it can be used as a time measuring equipment.

The length of a second pendulum at the surface of earth is $1\ m$. The length of second pendulum at the surface of moon, where $g$ is $\dfrac{1}{6} th$ that of earth's surface.

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

  1. $\dfrac{1}{6} m$

  2. $6 m$

  3. $\dfrac{1}{36}m$

  4. $36 m$

Show answer
Correct Option: A
Explanation:

We know that the time period of a second pendulum is $2s$ .

At earth ,
                $T=2\pi \sqrt{l _{e}/g _{e}}$
                $2=2\pi\sqrt{l _{e}/g _{e}}$
or             $g _{e}=\pi^{2}l _{e}$  ...............................eq1

At moon ,
                $T=2\pi \sqrt{l _{m}/g _{m}}$
or             $2=2\pi \sqrt{l _{m}/(g _{e}/6)}$  , given   $g _{m}=g _{e}/6$
or             $2=2\pi\sqrt{6l _{m}/\pi^{2}l _{e}}$   ,   putting the value of $g _{m}$ from  eq1
or             $l _{m}=l _{e}/6$
Now , given  $l _{e}=1m$

Hence ,     $l _{m}=1/6m$

The length of the simple pendulum which ticks seconds is:

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

  1. $0.5$m

  2. $1$m

  3. $1.5$m

  4. $2$m

Show answer
Correct Option: B
Explanation:

The time period of a simple pendulum is
$T = 2 \pi \sqrt{\dfrac{L}{g}}$
where L is the length of the pendulum.
or $ L = \dfrac{gT^2}{4 \pi^2}$
The time period of the simple pendulum which ticks seconds is $2$s.
$\therefore T = 2s$
Substituting in (i), we get


$L = \dfrac{(9.8 m s^{-2})(2s)^2}{4 \times (3.14)^2} = 1m$

A second's pendulum is mounted in a rocket. Its period of oscillation will decrease when the rocket is:

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

  1. moving up with uniform velocity

  2. moving up with uniform acceleration

  3. moving down with uniform acceleration

  4. moving around the earth in a geostationary orbit

Show answer
Correct Option: B
Explanation:

Correct answer= B

As the rocket accelerates upwards, pseudo force acts in the opposite direction of propagation.
=> Pseudo force acts in downward direction and gets added up to gravitational force.
=> Effective gravity= gravitational force+ pseudo force
                                >Gravitational force
=>             g'        >         g       where g' = effective gravity
Since time period of oscillation of pendulum= √(L/g)
       where L= length of the pendulum
                   g= gravitational force acting on the pendulum
=> In this situation,
          time period of oscillation of pendulum=√(L/g')
Since g' > g
=>     √(L/g')      <     √(L/g)
=>  Time period of oscillation decreases

When a rigid body is suspended vertically and it oscillates with a small amplitude under the action of the force of gravity, the body is known as

physics oscillatory motion a few applications of linear shm simple pendulum example of simple harmonic motion

  1. simple pendulum

  2. torsional pendulum

  3. compound pendulum

  4. seconds pendulum

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Correct Option: C
Explanation:

When a rigid body is suspended vertically, and it oscillates with a small amplitude under the action of the force of gravity, the body is known as compound pendulum. Thus the periodic time of a compound pendulum is minimum when the distance between the point of suspension and the centre of gravity is equal to the radius of gyration of the body about its centre of gravity.

The correct option is (c)

 The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from $10\ cm$ to $8\ cm$ In $40$ seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is $1.3$, the time In which amplitude of this pendulum will reduce from $10\ cm$ to $5\ cm$ in carbondioxide will be close to (in $5=1.601, \ln { 2 }  2=0.693$)

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

  1. $231\ s$

  2. $208\ s$

  3. $161\ s$

  4. $142\ s$

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Correct Option: C

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

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

  1. 20 s

  2. 50 s

  3. 40 s

  4. 5 s

Show answer
Correct Option: C
Explanation:

Time taken for 1 oscillation is 2 s
Time taken for 20 oscillations is $(2 \times 20) = 40  s$

A hollow pendulum bob filled with water has a small hole at the bottom through which water escapes at a constant rate. Which of the following statements describes the variation of the time period (T) of the pendulum as the water flows out?

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

  1. T decreases first and then increases.

  2. T increases first and then decreases.

  3. T increases throughout.

  4. T does not change.

Show answer
Correct Option: B
Explanation:

$\displaystyle T = 2\pi \sqrt{\frac{l}{g}}$
First distance of comfrom suspension point will increase then decrease.