Tag: physics

Questions Related to physics

At room temperature, if the relative permittivity of water be $80$ and the relative permeability be $0.0222$, then the velocity of light in water is ________ $m/{s}^{-1}$

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. $3\times { 10 }^{ 8 }\quad $

  2. $2.25\times { 10 }^{ 8 }$

  3. $2.5\times { 10 }^{ 8 }$

  4. $3.5\times { 10 }^{ 8 }$

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Correct Option: B
Explanation:

Formula 

$V=\cfrac{1}{\sqrt{\mu _0\epsilon _0}}\V^1=\cfrac{1}{\mu _r\epsilon _r}\ \Rightarrow \cfrac{V}{V^1}=\sqrt{\cfrac{\mu _r\epsilon _r}{\mu _0\epsilon _0}}$
$\Rightarrow\cfrac{V^1}{V}=\sqrt{\cfrac{\mu _0}{}{\mu _r}\times\cfrac{\epsilon _0}{\epsilon _r}}=\sqrt{\cfrac{1}{80}\times\cfrac{1}{0.0222}}\ \Rightarrow V^1=\sqrt{\cfrac{1}{80}\times\cfrac{1}{0.0222}}\times V\ \quad=\sqrt{\cfrac{1}{80}\times\cfrac{1}{0.022}}\times3\times10^8\ \quad=2.249\times 10^8\ \quad\approx2.22\times10^8m/s$

Surface charge density of a thin disc having radius $R$ varies with distance from centre as $\sigma =\sigma _{0}\dfrac {R}{r}(r\neq 0) $ then total charge of disc is

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. $2\pi \sigma _{0}R^{3}$

  2. $\sqrt {2}\pi \sigma _{0}R^{2}$

  3. $2\sqrt {2}\pi \sigma _{0}R^{2}$

  4. $2\pi \sigma _{0}R^{2}$

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Correct Option: A

A large box is accelerated up the inclined plane with an acceleration a and pendulum is kept vertical (Somehow by an external agent) as shown in figure.Now if the pendulum is set free to oscillate from such position, then what is the tension in the string immediately after the pendulum is set free? (mass of $500m$)

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

  1. $mg$

  2. $ma _{o} \sin\theta$

  3. $\left( m g + m a _ { 0 } \sin \theta \right)$

  4. Zero

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Correct Option: C

 The time period of oscillation of a torsional pendulum of moment of inertia I is

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

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

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

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

  4. $T =2 \pi \sqrt{I/4k}$

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Correct Option: A
Explanation:

The time period of oscillations of a torsional pendulum is $T =2 \pi \sqrt(I/k)$

The correct option is (a)

A bullet of mass $'m'$ hits a pendulum bob of mass $'2m'$ with a velocity $'v'$ and comes out of the bob with velocity $v/2$. Length of the pendulum is $2$ meter and $g=10 ms^{-2}$. The minimum value of $'v'$ for the bullet so that the bob may complete one revolution in the verticle is

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

  1. $40 ms^{-1}$

  2. $2.20 ms^{-1}$

  3. $3.15 ms^{-1}$

  4. $10 ms^{-1}$

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Correct Option: A

Time period of a disc about a tangent parallel to the diameter is same as the time period of a simple pendulum. The ratio of radius of disc to the length of pendulum is :

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

  1. $\dfrac { 1 } { 4 }$

  2. $\dfrac { 4 } { 5 }$

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

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

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Correct Option: C

A pendulum of mass $m$ hangs from a support fixed to a trolley. The direction of the string (i.e.., angle $\theta$) when the trolley rolls up a plane of inclination $\alpha$ with acceleration $'a'$ is

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

  1. Zero

  2. $\tan^{-1} \alpha$

  3. $\tan^{-1}\dfrac{a+g \sin \alpha}{g \cos \alpha}$

  4. $\tan^{-1}\dfrac{a}{g}$

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Correct Option: C

The oscillations of a pendulum slow down due to

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

  1. the force exerted by air and friction at the support

  2. the foce exerted by air only

  3. the forces exerted by friction at the support only

  4. none of these

Show answer
Correct Option: A
Explanation:

The pendulum slows down due to friction force exerted by air and friction at the support.

The pendulum of a certain clock has time period $2.04 s$. How fast or slow does the clock run during $24$ hour?

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

  1. $28.8$ minutes slow

  2. $28.8$ minutes fast

  3. $14.4$ minutes fast

  4. $14.4$ minutes slow

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Correct Option: A

A string of simple pendulum can bear maximum tension that is twice the weight of the bob. What is the maximum angle $(\theta)$ with which it can oscillate?

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

  1. $0^0$

  2. $45^0$

  3. $60^0$

  4. $90^0$

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Correct Option: B