Q. A graph is plotted between the temperature of a copper cube in ${ }^{\circ} C$ versus ${ }^{\circ} F$. The sine of the angle made by the graph with ${ }^{\circ} F$ axis is :

Thermal Properties of Matter Report Error

A

$\frac{2}{\sqrt{106}}$

B

$\frac{3}{\sqrt{106}}$

C

$\frac{4}{\sqrt{106}}$

D

$\frac{5}{\sqrt{106}}$

Solution:

$T_{C}=\frac{5}{9}\left(T_{F}-32\right)$
$T_{C}=\frac{5}{9} T_{F}-\frac{160}{9}$
Thus graph between ${ }^{\circ} C$ and ${ }^{\circ} F$ can be drawn as

From graph we have $\sin \theta=\frac{A C}{A B}=\frac{160 / 9}{\sqrt{\left(\frac{160}{9}\right)^{2}+(32)^{2}}}$
$\Rightarrow =\frac{160 \times 9}{9 \times 32 \sqrt{106}}=\frac{5}{\sqrt{106}}$

Questions from Thermal Properties of Matter

1. A hollow flask retains its shape on heating because

2. If the temperature difference on the two sides of a wall increases from $ 100{}^\circ C $ to $ 200{}^\circ C $ , its thermal conductivity

Rajasthan PMT 2007

3. The radiation emitted by a star $A$ is $10,000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $8000 \, K$ and $2000 \, K$ respectively. The ratio of the radii of the star $A$ and the sun is

NTA Abhyas 2020

4. A black body at $1373$ $℃$ emits maximum energy corresponding to a wavelength of $1.78$ microns. The temperature of the moon for which $\lambda _{m}=14$ micron would be

NTA Abhyas 2020

5. Steam is passed into $54\, gm$ of water at $30^{\circ} C$ till the temperature of mixture becomes $90^{\circ} C$. If the latent heat of steam is $536\, cal / gm$, the mass of the mixture will be

Physics Most Viewed Questions

1. A car starts from rest and accelerates at $5\, m / s ^{2}$ At $t=4\, s$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t =6\, s$ ? (Take $\left. g =10\, m / s ^{2}\right)$

NEET 2021 Motion in a Straight Line

2. If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{ E }{ G }$ has the dimensions of:

NEET 2021 Physical World, Units and Measurements

3. The de Broglie wavelength of an electron moving with kinetic energy of $144 \,eV$ is nearly

NEET 2020 Dual Nature of Radiation and Matter

4. A wheel with $20$ metallic spokes each $1\, m$ long is rotated with a speed of $120\, rpm$ in a plane perpendicular to a magnetic field of $0.4\, G$. The induced emf between the axle and rim of the wheel will be, $(1 G = 10^{-4}\, T)$

NEET 2020 Electromagnetic Induction

5. Calculate the acceleration of the block and trolly system shown in the figure The coefficient of kinetic friction between the trolly and the surface is $0.05. (g = 10 \,m/s^{2}$, mass of the string is negligible and no other friction exists

NEET 2020 Laws of Motion