Tag: physics

Questions Related to physics

Initially a black body at absolute temperature $T$ is kept inside a closed chamber at absolute temperature $T _{o}$. Now the chamber is slightly opened to allow sun rays to enter. It is observed that temperatures $T$ and $T _{o}$ remains constant.Which of the following statement is/are true?

physics energy production perfectly black body black-body radiation black body radiation

  1. The rate of emission of energy from the black body remains the same

  2. The rate of emission of energy from the black body increases

  3. The rate of absorption of energy by the black body increases.

  4. The energy radiated by the black body equals the energy absorbed by it

Show answer
Correct Option: A,D
Explanation:

It is given that the absolute temperatures of both the black body and the surroundings are constant with time, even after sunlight(radiation) is incident on it.

  • When a body absorbs radiation, its temperature increases
  • When a body emits radiation, its temperature decreases
Also the sun, being a source of infinite radiation(very large source of radiation).
We infer from this that the incident radiation should be of constant magnitude.
And if the temperature of the black body is a constant, that means it's emission and absorption of radiation are matched and equal. The absorption is of constant magnitude, because the sun's radiation is of constant value. Hence the emission is of constant value also and is equal to the absorption. The options follow.

An ideal black body at room temperature is thrown in a furnace. It is observed that

physics energy production perfectly black body black-body radiation black body radiation

  1. initially it is darkest body and at later time the brightest

  2. it is darkest body at all the times

  3. it cannot be distinguished at all the times

  4. initially it is the darkest body and at later times it cannot be distinguished

Show answer
Correct Option: D
Explanation:

Initially the black body is in bright environment. So, it appears dark and finally when its temperature becomes equal to temperature of furnace, it becomes invisible

A spherical body of area A and emissivity $e = 0.6$ is kept inside a perfectly black body. Total heat radiated by the body at temperature $T$ 

physics energy production perfectly black body black-body radiation black body radiation

  1. $ 0.8\ e\sigma AT^4$

  2. $ 0.4\ e\sigma AT^4$

  3. $ 0.6\ e\sigma AT^4$

  4. $ 1.0\ e\sigma AT^4$

Show answer
Correct Option: D
Explanation:
According to Stefan's Boltzman law, the thermal energy radiated by a black body radiator per second per unit area is proportional to fourth power of the absolute temperature and is given by
$\dfrac{P}{A} = \sigma T^4$ ..............(1)
For the hot bodies other than black body radiator equation (1) becomes,
$\dfrac{P}{A} = e \sigma T^4$
$P = e \sigma A T^4$ .................(2)
where, $e$ is the emissivity of the body.
Now, when such hot body is kept inside a perfectly black body, the total thermal radiation is the sum of emitted radiations (in open) and the part of incident radiations reflected from the walls of the perfectly black body. This will give black body radiations, hence the total radiations emitted by the body will be,
$P = 1.0 e \sigma A T^4$.

Emissivity of a perfect black body is

physics energy production perfectly black body black-body radiation black body radiation

  1. always $0$.

  2. always $1$.

  3. between $0$ and $1$.

  4. always $>1$.

Show answer
Correct Option: B
Explanation:
Emissivity of a perfect black body is always 1.
The best absorber is defined as the object which can absorb all the electromagnetic radiations falling upon it. The black body is not only a perfect absorber but it is also the best in emitting radiation. Also, a black bosy in thermal equlibrium has emissivity, $\epsilon=1$

Radiation coming from the hole of a Ferry's Black body is called 

physics energy production perfectly black body black-body radiation black body radiation

  1. black radiation.

  2. cavity radiation.

  3. Ferry's radiation.

  4. None of these

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Correct Option: B
Explanation:
$\rightarrow$ Radiation coming from the hole of ferry's black body is called cavity radiation because this black body is double walled evacuated spherical cavity whose inner wall is blackened

Which of the following is an example of a black body radiation?

physics energy production perfectly black body black-body radiation black body radiation

  1. The cooling of earth at night

  2. Solar radiations

  3. Heat currents from a black surface

  4. None of these

Show answer
Correct Option: A,B
Explanation:
The Earth is heated by the flux of energy it receives from sun and cools down by emitting infrared radiations to space. So we can say that cooling of earth is example of the black body radiation.
Sun has no solid surface, any radiation that hits the Sun is scattered and absorbed until it is completely lost. This makes the Sun very close to black bodies as far as absorption is concerned and as a result it would be reasonable to suppose that it is black body radiators.
So, the radiation of sun is the black body radiation.

The Wien's displacement law for a black body is
($T$ is the absolute temperature in $K$
$b$ is a constant of proportionality 
$e$ is the emissivity of the black body)

physics energy production perfectly black body black-body radiation black body radiation

  1. $\lambda _{max} T = b$

  2. $\lambda _{max} T = e$

  3. $\lambda _{max} b = T$

  4. None of these

Show answer
Correct Option: A
Explanation:
According to wein's displacement law there is inverse relation between $\lambda _{max}$ of radiation emitted by black body and its temperature (absolute)
$\lambda _{max}\; \alpha \; \cfrac{1}{T} \Rightarrow =b\cfrac{1}{T} \Rightarrow \lambda _{max} T=b$

A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of the magnetic field is

physics magnetic effect of electric current magnetic field lines due to current magnetic field due to current carrying conductor magnetic field on the axis of a toroid

  1. 4 B

  2. B/2

  3. B

  4. 2 B

Show answer
Correct Option: C
Explanation:

$\displaystyle B = \mu _0 N _0  i;   $

$B _1 = (\mu _0) \left ( \dfrac{N _0}{2} \right ) (2 i) $

$= \mu _0 N _0 i = B$


$\Rightarrow B _1 = B$

A wire 28 m long is bent into N turns of circular coil of diameter 14 cm forming a solenoid of length 60 cm. Calculate the magnetic field inside it when a current of 5 amp passed through it.  $(\mu _0 = 12.57 \times 10^{-7} m^{-1})$

physics magnetic effect of electric current magnetic field lines due to current magnetic field due to current carrying conductor magnetic field on the axis of a toroid

  1. $6.67 \times10^{-1} T$

  2. $6.67 \times10^{-4} T$

  3. $6.67 \times10^{4} T$

  4. $2.67 \times10^{-4} T$

Show answer
Correct Option: B
Explanation:

Given $d = 14 cm=0.14 m$    

           $l = 60cm = 0.6 m$

By the question, $N \times \pi d = 28 m.$

$N \times \pi \times 0.14 = 28$

$\displaystyle \therefore N = \dfrac{28}{0.14 \times \pi} = 63.66 turns$

$\displaystyle B = \mu _o   nI  =\mu _o  \dfrac{N}{l} I = 12.57 \times 10^{-7} \times \dfrac{63.66}{0.6} \times 5$

$=6.67 \times10^{-4} T$

The electric current in a circular coil of two turns produced a magnetic induction of $0.2 T$ at its centre. The coil is unwound and is rewound into a circular coil of four turns. The magnetic induction at the centre of the coil now is, in $T$ :
(if same current flows in the coil)

physics magnetic effect of electric current magnetic field lines due to current magnetic field due to current carrying conductor magnetic field on the axis of a toroid

  1. $0.2$

  2. $0.4$

  3. $0.6$

  4. $0.8$

Show answer
Correct Option: D
Explanation:

Coil is unwound and is rewound into a circular coil of 4 turns,
$\therefore $ $2\pi R=4\times 2\pi r$ 
$r=\dfrac{R}{4}$
$\left | B \right | =\dfrac{\mu _{0}I}{\dfrac{2R}{4}}$ $=0.2\times$ $4=0.8T$