Tag: angular simple harmonic motion

Questions Related to angular simple harmonic motion

Time period of a sample pendulum is T, time taken by it to complete 3/8 oscillations (in terms of distance traveled) is 

  1. $
    \cfrac { 3 T } { 12 }
    $

  2. $
    \cfrac { 3 T } { 8 }
    $

  3. $
    \cfrac { 7 T } { 12 }
    $

  4. $
    \cfrac { 5 T } { 12 }
    $


Correct Option: D

A metallic disc oscillates about an axis through its edge in it's own plane. The equivalent length of the disc as a pendulum is

  1. $r$

  2. $\dfrac r3$

  3. $\dfrac { r } { 2 }$

  4. $\dfrac { 3r } { 2 }$


Correct Option: D

The bob of a simple pendulum executes  $S H M$  in water with a period  $t,$  while the period of oscillation of the bob is  $t _{ 0 }$  in air. Neglecting the frictional force of water and given that the density of the bob is  $( 4 / 3 ) \times 1000 kg / { m } ^ { 3 }.$  What relationship between  $t$  and  $t _ { 0 }$  is true ?

  1. $t = t _ { 0 }$

  2. $t = 4 t _ { 0 }$

  3. $t = 2 t _ { 0 }$

  4. $t = t _ { 0 } / 2$


Correct Option: C

A simple pendulum is released when $\theta = \pi/6$. The time period of oscillation is

  1. $\displaystyle 2\pi\sqrt{\frac{l}{g}}$

  2. $\displaystyle 2\pi\sqrt{\frac{l}{g}}\left(\frac{293}{288}\right)$

  3. $\displaystyle 2\pi\sqrt{\frac{l}{g}}\left(\frac{288}{293}\right)$

  4. none of these


Correct Option: B
Explanation:

For large amplitudes, the time period is given by 
$T={2\pi }{\sqrt{\dfrac{L}{g}}}(1+\dfrac{\theta ^{2}}{16})$
Substitute $\theta =\dfrac{\pi }{6}$, we get answer as 
$T={2\pi }{\sqrt{\dfrac{L}{g}}}(\dfrac{293}{288})$
Option B is correct.

A pendulum suspended from the ceiling of an elevator at rest has time period ${ T } _{ 1 }$. When the elevator moves up with an acceleration 'a' its time period of oscillation becomes ${ T } _{ 2 }$ when the elevator moves down with an acceleration 'a', its period of oscillation become ${ T } _{ 3 }$ then

  1. ${ T } _{ 1 }=\sqrt { { T } _{ 2 }{ T } _{ 3 } } $

  2. ${ T } _{ 1 }=\sqrt { T _{ 2 }{ ^{ 2 }T _{ 3 } }^{ 2 } } $

  3. ${ T } _{ 1 }=\dfrac { \sqrt { 2 } { T } _{ 2 }{ T } _{ 3 } }{ \sqrt { {T _{ 2 }}^{ 2 }+{T _{ 3 } }^{ 2 } } } $

  4. ${ T } _{ 1 }=\dfrac { { T } _{ 2 }{ T } _{ 3 } }{ \sqrt { {T _{ 2 }}^{ 2 }+{T _{ 3 } }^{ 2 } } } $


Correct Option: D

The centripetal acceleration of the bob of a conical pendulem is......................

  1. $\dfrac{mg}{cos \theta}$

  2. $\dfrac{rg}{L}$

  3. $\dfrac{g}{L}$

  4. $\dfrac{g}{L cos \theta}$


Correct Option: A

The time period of a torsional pendulum is

  1. $T=\pi\sqrt{C/I}$

  2. $T=2\pi\sqrt{I/C}$

  3. $T=2\pi\sqrt{C/I}$

  4. $T=\pi\sqrt{I/C}$


Correct Option: B
Explanation:

In torsional pendulum, $\omega =\sqrt{\frac{C}{I}}$
$T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{I}{C}}$
Option B is correct.

In a conical pendulum, when the bob moves in a horizontal circle of radius r, with uniform speed V, the string of length L describe a cone of semi-vertical angle $\theta$. The tension  in the string is given by 

  1. $T = \dfrac{mgl}{(L^2 - r^2)}$

  2. $ T = \dfrac{\sqrt {L^2 - r^2}}{mgl}$

  3. $ T = \dfrac{mgL}{\sqrt {L^2 - r^2}}$

  4. $ T = \dfrac{mgL}{(L^2 - r^2)^2}$


Correct Option: C

A seconds pendulum is attached to roof of car that is moving with acceleration $10{ m/s }^{ 2 }$ a straight road. Its frequency of oscillation 

  1. $\dfrac { 1 }{ 2 } Hz$

  2. $1Hz$

  3. $\dfrac { 1 }{ \sqrt { 2 } } Hz$

  4. ${ 2 }^{ -1/4 }Hz$


Correct Option: D

A simple pendulum in which the bob swings in a horizontal circle is called.

  1. Compound pendulum

  2. Horizontal pendulum

  3. Conical pendulum

  4. Gallitzin pendulum


Correct Option: C