Find the ratio of lengths of an iron rod and an aluminium rod
Question: Find the ratio of lengths of an iron rod and an aluminium rod for which the difference in the lengths is independent of temperature. Coefficients of linear expansion of iron and aluminium are $12 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $23 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ respectively. Solution:...
Read More →The density of water at
Question: The density of water at $0^{\circ} \mathrm{C}$ is $0.998 \mathrm{~g} / \mathrm{cm}^{3}$ and at $4^{\circ} \mathrm{C}$ is $1.00 \mathrm{~g} / \mathrm{cm}^{3}$. Calculate the average coefficient of volume expansion of water in the temperature range 0 to $4^{\circ} \mathrm{C}$. Solution:...
Read More →A metal scale made of steel reads accurately at
Question: A metal scale made of steel reads accurately at $20^{\circ} \mathrm{C}$. In a sensitive experiment, distances accurate up to $0.055 \mathrm{~mm}$ in $1 \mathrm{~m}$ are required. Find the range of temperature in which the experiment can be performed with this meter scale. Coefficient of linear expansion $=11 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ Solution:...
Read More →A meter scale is made up of steel and measures correct length
Question: A meter scale is made up of steel and measures correct length at $16^{\circ} \mathrm{C}$. What will be the percentage error if this scale is used (a) on a summer day when the temperature is $46^{\circ} \mathrm{C}$ and (b) on a winter day when the temperature is $6^{\circ} C_{\text {? Coefficient of linear expansion of steel }=11} \times 10^{-6} /{ }^{\circ} \mathrm{C}$ Solution:...
Read More →Two metre scales, one of steel and the other of aluminium,
Question: Two metre scales, one of steel and the other of aluminium, agree at $20^{\circ} \mathrm{C}$. Calculate the ratio aluminiumcentimetre/steel-centimeter at (a) $0^{\circ} \mathrm{C}$, (b) $40^{\circ} \mathrm{C}$ and (c) $100^{\circ} \mathrm{C}$. a for steel=1.1 $\times 10^{-5} /{ }^{\circ} \mathrm{C}$ and for aluminium $=2.3^{\times 10^{-5}} /{ }^{\circ} \mathrm{C}$. Solution:...
Read More →A circular hole of diameter 2.00 cm is made in an aluminium,
Question: A circular hole of diameter $2.00 \mathrm{~cm}$ is made in an aluminium, plate at $0^{\circ}$ C. What will be the diameter at $100^{\circ} \mathrm{C}$ ? a for aluminium $=2.3^{\times 10^{-5} /{ }^{\circ} \mathrm{C}}$ Solution:...
Read More →A railway track (made of iron) is laid in winter when the average temperature
Question: A railway track (made of iron) is laid in winter when the average temperature is $18^{\circ} \mathrm{C}$. The track consists of sections of $12.0 \mathrm{~m}$ placed one after the other. How much gap should be left between two much sections so that there is no compression during summer when the maximum temperature goes to $48^{\circ} \mathrm{C}$ ? Co-efficient of linear expansion of iron=11 $\times 10^{-6} /{ }^{\circ} \mathrm{C}$. Solution:...
Read More →A meter scale made of steel is calibrated at
Question: A meter scale made of steel is calibrated at $20^{\circ} \mathrm{C}$ to give correct reading. Find the distance between 50 $\mathrm{cm}$ mark and $51 \mathrm{~cm}$ mark if the scale is used at $10^{\circ}$ C. Co-efficient of linear expansion of steel is $1.1 \times 10^{-5}$ $/^{\circ} \mathrm{C}$ Solution:...
Read More →A concrete slab has a length of 10 m on a winter night
Question: A concrete slab has a length of $10 \mathrm{~m}$ on a winter night when the temperature is $0^{\circ} \mathrm{C}$. Find the length of the slab on a summer day when the temperature is $35^{\circ}$. The co-efficient of linear expansion of concrete is $1.0 x^{10^{-5}} /{ }^{\circ} \mathrm{C}$ Solution:...
Read More →A resistance thermometer reads
Question: A resistance thermometer reads $R=20.0 \Omega, 27.5 \Omega$ and $50.0 \Omega$ at the ice point $\left(0^{\circ} \mathrm{C}\right)$, the steam point ( $100^{\circ} \mathrm{C}$ ) and the zinc point $\left(420^{\circ} \mathrm{C}\right)$ respectively. Assuming that the resistance varies with the temperature as $R_{e}=R_{0}\left(1+\alpha \theta+\beta \theta^{2}\right)$, find the values of $R_{0}, \alpha$ and $\beta$. Here $\theta$ represents the temperature on Celsius scale. Solution:...
Read More →A platinum resistance thermometer reads
Question: A platinum resistance thermometer reads $0^{\circ}$ when its resistance is $80 \Omega$ and $100^{\circ}$ when its resistance is $90 \Omega$. Find the temperature at the platinum scale at which the resistance is $86 \Omega .$ Solution:...
Read More →In a Callender's compensated constant air pressure thermometer,
Question: In a Callender's compensated constant air pressure thermometer, the volume of the bulb is 1800 cc. When the bulb is kept immersed in a vessel, 200 cc of mercury has to be poured out. Calculate the temperature of the vessel. Solution:...
Read More →The pressure of the gas in a constant volume
Question: The pressure of the gas in a constant volume gas thermometer are $80 \mathrm{~cm}, 90 \mathrm{~cm}$ and $100 \mathrm{~cm}$ of mercury at the ice point, the steam point and in a heated wax bath respectively. Find the temperature of the wax bath. Solution:...
Read More →The pressure of the gas in a constant volume gas thermometer
Question: The pressure of the gas in a constant volume gas thermometer is $70 \mathrm{kPa}$ at the ice point. Find the pressure at the steam point. Solution:...
Read More →The pressure measured by a constant volume gas thermometer is
Question: The pressure measured by a constant volume gas thermometer is $40 \mathrm{kPa}$ at the triple point of water. What will be the pressure measured at the boiling point of water $\left(100^{\circ} \mathrm{C}\right)$ ? Solution:...
Read More →A gas thermometer measure the temperature from
Question: A gas thermometer measure the temperature from the variation of pressure of a sample of gas. If the pressured measured at the melting point of lead is $2.20$ times the pressure measured at the triple point of water, find the melting point of lead? Solution:...
Read More →A constant volume thermometer registers a pressure of
Question: A constant volume thermometer registers a pressure of $1.500 \times 10^{4} \mathrm{~Pa}$ at the triple point of water and a pressure of $2.050 \times 10^{4} \mathrm{~Pa}$ at the normal boiling point. What is the temperature at the normal boiling point? Solution:...
Read More →The steam point and the ice point of a mercury thermometer are
Question: The steam point and the ice point of a mercury thermometer are marked as $80^{\circ}$ and $20^{\circ}$. What will be the temperature in centigrade mercury scale when this thermometer reads $32^{\circ}$ ? Solution:...
Read More →Two light source of intensities 8 cd and 12 cd are placed
Question: Two light source of intensities 8 cd and 12 cd are placed on the same side of a photometer screen at a distance of $40 \mathrm{~cm}$ from it. Where should a $80 \mathrm{~cd}$ source be placed to balance the illuminance? Solution:...
Read More →An electric lamp and a candle produce equal
Question: An electric lamp and a candle produce equal illuminance at a photometer screen when they are placed at $80 \mathrm{~cm}$ and $20 \mathrm{~cm}$ from the screen respectively. The lamp is now covered with a thin paper which transmits $49 \%$ of the luminous flux. By what distance should the lamp be moved to balance the intensities at the screen again? Solution:...
Read More →Figure shows a small diffused plane source S
Question: Figure shows a small diffused plane source $S$ placed over a horizontal table- top at a distance of $2.4 \mathrm{~m}$ with its plane parallel to the table-top. The illuminance at the point A directly below the source is 25 lux. Find the illuminance at a point $B$ of the table at a distance of $1.8 \mathrm{~m}$ from A. Solution:...
Read More →A student is studying a book placed near the edge
Question: A student is studying a book placed near the edge of a circular table of radius R. A point source of light is suspended directly above the center of the table. What should be the height of the source above the table so as to produce maximum illuminance at the position of the book? Solution:...
Read More →Light from point source falls on a small area placed
Question: Light from point source falls on a small area placed perpendicular to the incident light. If the area is rotated about the incident light by an angle of $60^{\circ}$, by what fraction will illuminance change? Solution:...
Read More →A point source emitting light uniformly in all directions
Question: A point source emitting light uniformly in all directions is placed $60 \mathrm{~cm}$ above a table-top. The illuminance at a point on the table-top, directly below the source, is $15 l u x$. Find the illuminance at a point on the tabletop $80 \mathrm{~cm}$ away from the first point. Solution:...
Read More →The illuminance of a small area changes from
Question: The illuminance of a small area changes from 900 lumen/ $\mathrm{m}^{2}$ to 400 lumen/ $\mathrm{m}^{2}$ when it is shifted along its normal by $10 \mathrm{~cm}$. Assuming that it is illuminated by a point source placed on the normal. Find the distance between the source and the area in the original position. Solution:...
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