Tag: physics

Questions Related to physics

When a ceiling fan is switched off, its angular velocity reduces by $50$% while it makes $36$ rotations. How many more rotations will it make before coming to rest? (Assume uniforms angular retardation)

physics turning on a pivot the turning of couple couple turning effect of force the turning effect of a force moment of force or torque

  1. $48$

  2. $36$

  3. $12$

  4. $18$

Show answer
Correct Option: C
Explanation:

$\begin{array}{l} You\, \, have\, \, to\, \, use\, \, the\, \, equation, \ \; { { { \omega  } }^{ { 2 } } }\; ={ { { \omega  } } _{ { 0 } } }^{ { 2 } }\; +{ { 2\alpha \theta  } }\; \, \, for\, \, finding\, \, the\, \, angular\, \, acceleration\; \, \alpha \, \, and \ hence\, \, the\, \, number\, \, of\, \, further\, \, rotations. \ Note\, \, that\, \, this\, \, equation\, \, is\, \, the\, \, rotational\, \, analogue\, \, of\, \, the\, equation \ { v^{ 2 } }\; ={ v _{ 0 } }^{ 2 }+2as{ {  } }(or,\; { v^{ 2 } }\; ={ u^{ 2 } }\; +2as)\, \, in\, \, linear\, \, motion. \ Since\, \, the\, \, angular\, \, velocity\, \, has\, \, reduce\, \, to\, \, half\, \, of\, \, the\, \, initial\, \, value\, \, { \omega _{ 0 } }\, \, after\, \, 36\, \, rotations,\, \, we\, \, have \ { \left( { { \omega _{ 0\;  } }/2 } \right) _{ \;  } }^{ 2 }={ \omega _{ 0 } }^{ 2 }+2\alpha \times 36\, \, from\, \, which\, \; \alpha =--\; { \omega _{ 0 } }^{ 2 }/96 \ \left[ { We\, \, have\, \, expressed\, \, the\, \, angular\, \, displacement\, \, \theta \, \, in\, \, rotations\, \, itself\, \, for\, \, convenience } \right]  \ If\, \, the\, \, additional\, \, number\, \, of\, \, rotations\, \, is\, \, x,\, \, we\, \, have \ 0={ \left( { { \omega _{ 0\;  } }/2 } \right) _{ \;  } }^{ 2 }\; +\; 2\alpha x\; =\; { \left( { { \omega _{ 0\;  } }/2 } \right) _{ \;  } }^{ 2 }\; +\; 2\times (--\; { \omega _{ 0 } }^{ 2 }/96)x \ This\, \, gives, \ x\; =12 \end{array}$

Hence,
option $(C)$ is correct answer.

The minimum value of ${ \omega  } _{ 0 }$ below which the ring will drop down is 

physics turning on a pivot the turning of couple couple turning effect of force the turning effect of a force moment of force or torque

  1. $\sqrt { \dfrac { g }{ 2\mu (R-r) } } $

  2. $\sqrt { \dfrac { 3g }{ 2\mu (R-r) } } $

  3. $\sqrt { \dfrac { g }{ \mu (R-r) } } $

  4. $\sqrt { \dfrac { 2g }{ \mu (R-r) } } $

Show answer
Correct Option: C

a flywheel is in the form of a solid circular wheel of mass 72 kg and radius 50cm and it makes 70 r.p.m. then the energy of revolution is:

physics turning on a pivot the turning of couple couple turning effect of force the turning effect of a force moment of force or torque

  1. 245534 J

  2. 24000 J

  3. 4795000J

  4. 4791600 J

Show answer
Correct Option: D
Explanation:

$K.E=\cfrac{1}{2}mv^2\rightarrow(1)\v=r\omega$

Put in $(1)$
$K.E=\cfrac{1}{2}mr^2\omega^2$
Given data,
$m=72kg\r=50cm\ \omega=70rev/min$
$1rev=2\pi rad\1min=60sec\ \omega=\cfrac{70\times2\pi}{60}=2.33\times3.14\ \omega=7.3rad/sec$
So, $K.E=\cfrac{1}{2}mr^2\omega^2\Rightarrow\cfrac{1}{2}\times72\times50\times50\times\cfrac{7.3}{10}\times\cfrac{7.3}{10}\ K.E=4791600J$

Two discs having masses in the ratio $1:2$ and radii in the ratio $1:8$ roll down without slipping one by one from an inclined plane of height $h$. The ratio of their linear velocities on reaching the ground is

physics turning on a pivot the turning of couple couple turning effect of force the turning effect of a force moment of force or torque

  1. $1:16$

  2. $1:128$

  3. $1:8\sqrt{2}$

  4. $1:1$

Show answer
Correct Option: D

An electrical device draws 2 kW power from ac mains voltage 223 V(rms). The current differs lags in phase by $\phi = tan^{-1} \left ( -\frac{3}{4} \right )$ as compared to voltage. The resistance R in the circuit is:

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. 15 $\Omega$

  2. 20 $\Omega$

  3. 25 $\Omega$

  4. 30 $\Omega$

Show answer
Correct Option: B
Explanation:

Here, $P \, = \, 2 \, kW \, = \, 2 \, \times \, 10^3W$
$V _{rms} \, = \, 233 \, V, tan \, \phi \, = \, -\dfrac{3}{4}$
$As, \, P \, = \, \dfrac{V^2 _{rms}}{Z}$

$\Rightarrow \, Z \, = \, \dfrac{V^2 _{rms}}{P} \, = \, \dfrac{(223)^2}{2000} \, =  \dfrac{49729}{2000} \, = \, 24.86 \, \Omega \, or \, Z \, = \, 25 \, \Omega$

$\tan \, \phi \, = \, \dfrac{X _C \, - \, X _L}{R} \, = \, - \dfrac{3}{4} \, \therefore \, X _C \, - \, X _L \, = \, -\dfrac{3}{4} R.$

AS, $Z^2 \, = \, R^2 \, + \, (X _C \, - \, X _L)^2$
$\therefore \, (25)^2 \, = \, R^2 \, + \, \left(-\dfrac{3}{4} \, R \right)^2$
$625 \, = \, \dfrac{25 \, R^2}{16}.$
$R^2 \, = \, \dfrac{625 \, \times \, 16}{25} \,  \, \Rightarrow \, R \, = \, 20 \, \Omega$

A voltage of peak value 283 V and varying frequency is applied to series LCR combination in which R = 3$\Omega$, L = 25 mH and C = 400$\mu$F. Then the frequency (in Hz) of the source at which maximum power is dissipated in the above is

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. 51.5

  2. 50.7

  3. 51.1

  4. 50.3

Show answer
Correct Option: D
Explanation:

Here, $V _0 \, = \, 283 \, V, \, R \, = \, 3\Omega, \, L \, = \, 25 \, \times \, 10^{-3} \, H$
$C \, = \, 400 \, \mu F \, = \, 4 \, \times \, 10^{-4} F$
Maximum power is dissipated at resonance, for which 

$\nu \, = \, \dfrac{1}{2\pi \sqrt{LC}} \, = \, \dfrac{1 \, \times \, 7}{2 \, \times \, 22 \, \sqrt{25 \, \times \, 10^{-3} \, \times \, 4 \, \times \, 10^{-4}}}$

$= \, \dfrac{7 \, \times \, 10^3}{44\sqrt{10}} \, = \, 50.3 \, Hz$

Power dissipated in pure inductance will be

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. $\dfrac {LI^{2}}{2}$

  2. $2LI^{2}$

  3. $\dfrac {LI^{2}}{4}$

  4. Zero

Show answer
Correct Option: D
Explanation:

Power is dissipated only in the Resistor , Capacitor and Inductor only store  energy. So Inductance power dissipated is Zero.

A coil has a resistance $ 10 \Omega $ and an inductance of 0.4 henry. It is connected to an AC source of $ 6.5 V , \frac {30} { \pi } Hz. $ The average power consumed in the circuit, is :

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. $ \cfrac {5} { 8} W $

  2. $ \cfrac {4} {3} W $

  3. $ \cfrac {3} {8} W $

  4. $ \cfrac {6} {7} W $

Show answer
Correct Option: A

The power loss in an $AC$ circuit is $E _{rms}$ $I _{rms}$, when in the circuit there is only

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. $C$

  2. $L$

  3. $R$

  4. $L,\ C$ and $R$

Show answer
Correct Option: C
Explanation:

Inductors and capacitors bring a phase difference between the voltage and current in the circuit, hence changing the p.f. When only a resistance is present, $Poer\ factor= 1$.
The power loss in an AC circuit$ =E _{rms} I _{rms} Power\ factor $

The self inductance of the motor of an electric fan is 10 H. In order to impart maximum powr of 50 Hz, it should be connected to a capacitance of

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. $8\mu F$

  2. $4\mu F$

  3. $2\mu F$

  4. $1\mu F$

Show answer
Correct Option: D
Explanation:

Maximum power ($ I^2 R )$ is obtained when $I$ is maximum ( $Z$ is minimum).

For $Z$ minimum, $X _L=X _C$, which yields
$C=\dfrac {1}{(2\pi n)^2L}=\dfrac {1}{4\pi^2\times 50\times 50\times 10}$

$\therefore C=0.1\times 10^{-5}F=1\ \mu F$