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Questions Related to physics

The bob cf a simple pendulum is a spherical hollowe bal filled with water A pluyged hole near the bouthmol th oscilloting bob gets suddenly unplugged. During observation, till water is coming out, the time period of would 

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. First increase and then decrease to the original value

  2. first decrease and then increase to the original value

  3. remain unchanged

  4. none of these

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Correct Option: A

If the simple pendulum maximum kinetic energy of length 'I'  has maximum angular displacement $\theta $ then the maximum kinetic energy of the bob of mass 'm' is:

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $m g / ( 1 - \cos \theta )$

  2. $\operatorname { mg } l ( 1 - \sin \theta )$

  3. $m g / ( 1 + \cos \theta )$

  4. $m g l ( 1 + \sin \theta )$

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Correct Option: A

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

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

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

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

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

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

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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

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $r$

  2. $\dfrac r3$

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

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

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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 ?

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $t = t _ { 0 }$

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

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

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

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Correct Option: C

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

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  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

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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

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  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 } } } $

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Correct Option: D

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

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

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

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

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

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

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Correct Option: A

The time period of a torsional pendulum is

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

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

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

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

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

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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 

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  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}$

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Correct Option: C