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Multiple choice physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

A short linear object of length $b$ lies along the axis of a concave mirror of focal length $f$ at a distance u from the pole of the mirror. The size of the image is approximately equal to :

  1. $b\left (\dfrac {u-f}{f}\right )^{\dfrac {1}{2}}$
  2. $b\left (\dfrac {b}{u-f}\right )^{\dfrac {1}{2}}$
  3. $b\left (\dfrac {u-f}{f}\right )$
  4. $b\left (\dfrac {f}{u-f}\right )^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From mirror formula,


$\cfrac { 1 }{ v } +\cfrac { 1 }{ u } =\cfrac { 1 }{ f } \longrightarrow (1)$

Differentiating, we get  


$\Rightarrow -{ \upsilon  }^{ -2 }dv-{ u }^{ -2 }du=0$

or $\left| d\upsilon  \right| =\left| \cfrac { { \upsilon  }^{ 2 } }{ { u }^{ 2 } }  \right| du \ \longrightarrow (2)$         

Here $\left| dv \right| =$size of image,

$\left| du \right| =$size of object $\left( =b \right) $

From the equation $1$, we write

$\cfrac { u }{ v } +1 =\cfrac { u }{ f } $

Squaring both sides, we get

$\cfrac { { \upsilon  }^{ 2 } }{ { v }^{ 2 } } ={ \left( \cfrac { f }{ u-f }  \right)  }^{ 2 }$

Substituting in equation $2$ we get

Size of the image  $dv=b{ \left( \cfrac { f }{ u-f }  \right)  }^{ 2 }$

Multiple choice physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

Magnification for erect and invented image is

  1. $+ve$ and $-ve$ respectively
  2. $-ve$ and $+ve$ respectively
  3. $+ve$
  4. $-ve$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Magnification is the ratio of height of image and object .

And by convention , height of image formed below principal axis is taken negative and above is taken positive.

Hence, for erect image, $m=+ve$ and for inverted image $m=-ve$.

Answer-(A).

Multiple choice physics measurements and units kinds of units fundamental quantities standardized measurement

The SI unit of specific latent heat is 

  1. $Jkg^{-1}K^{-1}$
  2. $J^{0}K^{-1}$
  3. $J kg^{-1}$
  4. $J kgK^{-1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The specific latent heat of a substance is the quantity of heat energy required to change the state of a unit mass of a substance.

${E} _{L}= ml$

here ${E} _{L}$ is the heat transferred, in joules,m is the mass, in kilograms, and l is the latent heat in joules per kilogram.

The SI unit for specific latent heat is $J{kg}^{-1}$.

Multiple choice physics measurements and units kinds of units fundamental quantities standardized measurement

The specific heat capacity of water in SI unit is :

  1. $4.2 Jg^{-1}K^{-1}$
  2. $42 Jg^{-1}K^{-1}$
  3. $420 J kg^{-1}K^{-1}$
  4. $4200 J kg^{-1}K^{-1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The specific heat capacity  of a substance is the heat needed to raise

the temperature of 1 kg of the substance by 1K (or by ${1}^{0}C$).
The specific heat capacity of water is $4200 J{kg}^{-1}{K}^{-1}$.

Multiple choice physics measurements and units kinds of units fundamental quantities standardized measurement

The SI unit of thermal capacity is ;

  1. $J\ kg^{-1}\ K^{-1}$
  2. $J^{-1}\ kg\ K^{-1}$
  3. $JK^{-1}$
  4. $J\ kg\ K^{-1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation


The heat or thermal capacity of a defined system is the amount of heat required to raise the system's temperature by one degree. It is expressed in units of thermal energy per degree temperature.

$q= C\times t$

$C=\dfrac{q}{\triangle t}$

here,$C=$heat or thermal capacity
        $q=$heat required (J)
        $\triangle t={t} _{1}-{t} _{2}$ (K)

so,The S.I. unit of heat or thermal capacity is $J{K}^{-1}$

Multiple choice physics measurements and units kinds of units fundamental quantities standardized measurement

Column I gives three physical quantities. Select the appropriate units for these from the choices given in column II. Some of the physical quantities may have more than one choice.

Column-I Column - II
a) Capacitance d) Ohm second
b) Inductance e) Coulomb$^{2}$ joule$^{ -1 }$
c) Magnetic induction f) Coulomb volt$^{ -1 }$
g) Newton (ampere/metre)$^{ -1 }$
h) Volt second (ampere)$^{ -1 }$

  1. a-e,f; b-d,h; c-g

  2. a-h; b-d; c-e

  3. a-e; b-g,h; c-g

  4. a-e,f; b-d,h; c-d,e
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Capacitance is charge per unit volt. 

Volt has unit of work per unit chage. 
So capacitance has units of charge square per unit energy. 
Inductance is defined as volt per unit rate of change of current and voltage per unit current is resistance, so inductance is ohm second. 

Multiple choice physics measurements and units kinds of units fundamental quantities standardized measurement

The SI unit of magnetic permeability is

  1. ${ Am }^{ -1 }$
  2. ${ Am }^{ -2 }$
  3. ${ Hm }^{ -2 }$
  4. ${ Hm }^{ -1 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The correct option is D.

The magnetic permeability of any material is its property for allowing the magnetic line of force to pass through it. Therefore, the magnetic material can support the development of the magnetic field. This capability is measured by the magnetic permeability. Also, the magnetic line of force is directly proportional to the conductivity of the material. Its SI unit is Henry per meter i.e. $Hm^{-1}$ or newton per ampere square.