A bimetallic strip is made of aluminium and steel $\left(\alpha_{\mathrm{Al}}>\alpha_{\text {steel }}\right)$. On heating, the strip will

A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly

The graph between two temperature scales $A$ and $B$ is shown in figure between upper fixed point and lower fixed point there are 150 equal division on scale $A$ and 100 on scale $B$. The relationship for conversion between the two scales is given by

An aluminium sphere is dipped into water. Which of the following is true?

As the temperature is increased, the period of a pendulum

Heat is associated with

The radius of a metal sphere at room temperature $T$ is $R$ and the coefficient of linear expansion of the metal is $\alpha$. The sphere heated a little by a temperature $\Delta T$ so that its new temperature is $T+\Delta T$. The increase in the volume of the sphere is approximately.

A sphere, a cube and a thin circular plate, all of same material and same mass are initially heated to same high temperature.

Mark the correct options

Gulab namuns (assumed to be spherical) are to be heated in an oven. They are available in two sizes, one twice bigger (in radius) than the other. Pizzas (assumed to be discs) are also to be heated in oven. They are also in two sizes, one twice bigger (in radius) than the other. All four are put together to be heated to oven temperature. Choose the correct option from the following.

Refer to the plot of temperature versus time (figure) showing the changes in the state if ice on heating (not to scale). Which of the following is correct?

A glass full of hot milk is poured on the table. It begins to cool gradually. Which of the following is correct?

Is the bulb of a thermometer made of diathermic or adiabatic wall?

A student records the initial length $l$, change in temperature $\Delta T$ and change in length $\Delta l$ of a rod as follows

If the first observation is correct, what can you say about observation 2, 3 and 4.

Why does a metal bar appear hotter than a wooden bar at the same temperature? Equivalently it also appears cooler than wooden bar if they are both colder than room temperature.

Calculate the temperature which has numeral value on Celsius and Fahrenheit scale.

These days people use steel utensiles with copper bottom. This is supposed to be good for uniform heating of food. Explain this effect using the fact that copper is the better conductor.

Find out the increase in moment of inertia $I$ of a uniform rod (coefficient of linear expansion $\alpha$ ) about its perpendicular bisector when its temperature is slightly increased by $\Delta T$.

During summers in India, one of the common practice to keep cool is to make ice balls of crushed ice, dip it in flavoured sugar syrup and sip it. For this a stick is inserted into crushed ice and is squeezed in the palm to make it into the ball. Equivalently in winter in those areas where it snows, people make snow balls and throw around. Explain the formation of ball out of crushed ice or snow in the light of $p-T$ diagram of water.

100 g of water is supercooled to $-10^{\circ} \mathrm{C}$. At this point, due to some disturbance mechanised or otherwise some of it suddenly freezes to ice. What will be the temperature of the resultant mixture and how much mass would freeze? $\left[S_w=1 \mathrm{cal} / \mathrm{g} /{ }^{\circ} \mathrm{C}\right.$ and $\left.L_{\text {Fusion }}^w=80 \mathrm{cal} / \mathrm{g}\right]$

One day in the morning. Ramesh filled up $1 / 3$ bucket of hot water from geyser, to take bath. Remaining $2 / 3$ was to be filled by cold water (at room temperature) to bring mixture to a comfortable temperature. Suddenly Ramesh had to attend to something which would take some times, say 5-10 min before he could take bath. Now, he had two options (i) fill the remaining bucket completely by cold water and then attend to the work, (ii) first attend to the work and fill the remaining bucket just before taking bath. Which option do you think would have kept water warmer? Explain

We would like to prepare a scale whose length does not change with temperature. It is proposed to prepare a unit scale of this type whose length remains, say 10 cm . We can use a bimetallic strip made of brass and iron each of different length whose length (both components) would change in such a way that difference between their length $B$ remain constant. If $\alpha_{\text {iron }}=1.2 \times 10^{-5} / \mathrm{K}$ and $\alpha_{\text {brass }}=1.8 \times 10^{-5} / \mathrm{K}$, what should we take as length of each strip?

We would like to make a vessel whose volume does not change with temperature (take a hint from the problem above). We can use brass and iron $\left(\beta_{\text {vbrass }}=6 \times 10^{-5} / K\right.$ and $\left.\beta_{\text {viron }}=3.55 \times 10^{-5} / \mathrm{K}\right)$ to create a volume of 100 cc . How do you think you can achieve this?

Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of $57^{\circ} \mathrm{C}$ is drunk. You can take body (tooth) temperature to be $37^{\circ} \mathrm{C}$ and $\alpha=1.7 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ bulk modulus for copper $=140 \times 10^9 \mathrm{~N} / \mathrm{m}^2$

A rail track made of steel having length 10 m is clamped on a railway line at its two ends (figure). On a summer day due to rise in temperature by $20^{\circ} \mathrm{C}$. It is deformed as shown in figure. Find $x$ (displacement of the centre) if $\alpha_{\text {steel }}=1.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}$.

A thin rod having length $L_0$ at $0^{\circ} \mathrm{C}$ and coefficient of linear expansion $\alpha$ has its two ends maintained at temperatures $\theta_1$ and $\theta_2$, respectively. Find its new length.

According to Stefan's law of radiation, a black body radiates energy $\sigma T^4$ from its unit surface area every second where $T$ is the surface temperature of the black body and $\sigma=5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}^4$ is known as Stefan's constant. A nuclear weapon may be thought of as a ball of radius 0.5 m . When detonated, it reaches temperature of $10^6 \mathrm{~K}$ and can be treated as a black body.

(a) Estimate the power it radiates.

(b) If surrounding has water at $30^{\circ}$, how much water can $10 \%$ of the energy produced evaporate in 1 s ?

$$\left[S_w=4186.0 \mathrm{~J} / \mathrm{kg} \mathrm{K} \text { and } L_v=22.6 \times 10^5 \mathrm{~J} / \mathrm{kg}\right]$$

(c) If all this energy $U$ is in the form of radiation, corresponding momentum is $p=U / c$. How much momentum per unit time does it impart on unit area at a distance of 1 km ?