In an experiment of measuring the refractive | vedclass

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(B) The refractive index is given by $\mu = \frac{h}{h'}$,where $h = 5.25\,mm$ and $h' = 5.00\,mm$.The main scale division $(MSD)$ is $\frac{1}{20}\,c

Vedclass · Accepted Answer

$41$

Vedclass · Answer

(B) The refractive index is given by $\mu = \frac{h}{h'}$,where $h = 5.25\,mm$ and $h' = 5.00\,mm$.The main scale division $(MSD)$ is $\frac{1}{20}\,cm = 0.5\,mm$.The least count $(LC)$ of the travelling microscope is $1\,MSD - 1\,VSD = 1\,MSD - \frac{49}{50}\,MSD = \frac{1}{50}\,MSD = \frac{0.5\,mm}{50} = 0.01\,mm$.Taking the natural logarithm of the refractive index formula: $\ln \mu = \ln h - \ln h'$.Differentiating,we get the relative uncertainty: $\frac{d\mu}{\mu} = \frac{dh}{h} + \frac{dh'}{h'}$.Here,$dh = dh' = LC = 0.01\,mm$.Substituting the values:$d\mu = \mu \left( \frac{dh}{h} + \frac{dh'}{h'} ight) = \left( \frac{5.25}{5.00} ight) \left( \frac{0.01}{5.25} + \frac{0.01}{5.00} ight)$.$d\mu = \frac{0.01}{5.00} + \frac{0.01}{5.25} = 0.002 + 0.00190476 = 0.00390476$.$d\mu \approx 3.90476 	imes 10^{-3} = \frac{39.0476}{10} 	imes 10^{-3} \approx \frac{41}{10} 	imes 10^{-3}$ (rounding to the nearest integer for $x$).Thus,$x = 41$.

List-$I$	List-$II$
$(A)$ Mass density	$(I)$ $[ML^2T^{-3}]$
$(B)$ Impulse	$(II)$ $[MLT^{-1}]$
$(C)$ Power	$(III)$ $[ML^2T^0]$
$(D)$ Moment of inertia	$(IV)$ $[ML^{-3}T^0]$

List-$I$	List-$II$
$(a)$ Torque	$(i)$ ${MLT}^{-1}$
$(b)$ Impulse	$(ii)$ ${MT}^{-2}$
$(c)$ Tension	$(iii)$ ${ML}^{2} {T}^{-2}$
$(d)$ Surface Tension	$(iv)$ ${ML} {T}^{-2}$

Similar Questions

Match List-$I$ with List-$II$.
List-$I$ List-$II$
$(A)$ Mass density $(I)$ $[ML^2T^{-3}]$
$(B)$ Impulse $(II)$ $[MLT^{-1}]$
$(C)$ Power $(III)$ $[ML^2T^0]$
$(D)$ Moment of inertia $(IV)$ $[ML^{-3}T^0]$
Choose the correct answer from the options given below:

Match List-$I$ with List-$II$.
List-$I$ List-$II$
$(a)$ Torque $(i)$ ${MLT}^{-1}$
$(b)$ Impulse $(ii)$ ${MT}^{-2}$
$(c)$ Tension $(iii)$ ${ML}^{2} {T}^{-2}$
$(d)$ Surface Tension $(iv)$ ${ML} {T}^{-2}$

Choose the most appropriate answer from the options given below:

The speed of light in vacuum is taken as unity. If light takes $6 \text{ min } 40 \text{ s}$ to reach the Earth from the Sun,the distance between the Sun and the Earth in new units is:

Of the following quantities,which one has dimensions different from the remaining three?

The diameter and height of a cylinder are measured by a meter scale to be $12.6 \pm 0.1\, cm$ and $34.2 \pm 0.1\, cm$,respectively. What will be the value of its volume in appropriate significant figures?

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