Tag: physics

Quizzes (598) Questions (13441)

Questions Related to physics

Multiple choice 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

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)

  1. $48$

  2. $36$

  3. $12$

  4. $18$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

Multiple choice 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

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

  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) } } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This relates to the critical angular velocity required for a ring to maintain contact or prevent slipping in a rotating system. The derivation leads to the expression in option C.

Multiple choice 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

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:

  1. 245534 J

  2. 24000 J

  3. 4795000J

  4. 4791600 J
Reveal answer Fill a bubble to check yourself
D Correct answer
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, $K.E=\cfrac{1}{2}mr^2\omega^2\Rightarrow\cfrac{1}{2}\times72\times50\times50\times\cfrac{7.3}{10}\times\cfrac{7.3}{10}\ K.E=4791600J$

Multiple choice 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

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

  1. $1:16$

  2. $1:128$

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

  4. $1:1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a disc rolling down an incline, the final linear velocity v = sqrt(2gh / (1 + k^2/R^2)). For a uniform disc, k^2/R^2 = 0.5. Since the velocity depends only on height h and the shape (moment of inertia factor), the mass and radius do not affect the final velocity. Thus, the ratio is 1:1.

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

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:

  1. 15 $\Omega$

  2. 20 $\Omega$

  3. 25 $\Omega$

  4. 30 $\Omega$
Reveal answer Fill a bubble to check yourself
B Correct answer
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, $Z^2 \, = \, R^2 \, + \, (X _C \, - \, X _L)^2$
$\therefore \, (25)^2 \, = \, R^2 \, + \, \left(-\dfrac{3}{4} \, R \right)^2$
$625 \, = \, \dfrac{25 \, R^2}{16}.$
$R^2 \, = \, \dfrac{625 \, \times \, 16}{25} \,  \, \Rightarrow \, R \, = \, 20 \, \Omega$

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

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

  1. 51.5

  2. 50.7

  3. 51.1

  4. 50.3
Reveal answer Fill a bubble to check yourself
D Correct answer
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 

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

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

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

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 :

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

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

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

  4. $ \cfrac {6} {7} W $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The impedance Z = sqrt(R^2 + XL^2). XL = 2 * pi * f * L = 2 * pi * (30/pi) * 0.4 = 24 ohms. Z = sqrt(10^2 + 24^2) = sqrt(100 + 576) = 26 ohms. Current I = V/Z = 6.5 / 26 = 0.25 A. Power P = I^2 * R = (0.25)^2 * 10 = 0.0625 * 10 = 0.625 W, which is 5/8 W.

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

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

  1. $C$

  2. $L$

  3. $R$

  4. $L,\ C$ and $R$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $

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

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

  1. $8\mu F$

  2. $4\mu F$

  3. $2\mu F$

  4. $1\mu F$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

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

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