Answer: The wire is stretched both from the end so the frequency of stretched wire is as follows: $ v=\frac{n}{2L}\sqrt{\frac{T}{m}} $ As the number of harmonic n, length L, and tension (T) are kept...
According to Stefan’s law of radiation, a black body radiates energy σT4 from its unit surface area every second where T is the surface temperature of the black body and σ = 5.67 × 10-8 W/m2K4 is known as Stefan’s constant. A nuclear weapon may be thought of as a ball of radius 0.5 m. When denoted, it reaches temperature of 106K and can be treated as a black body.
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? Answer: (c) According to...
According to Stefan’s law of radiation, a black body radiates energy σT4 from its unit surface area every second where T is the surface temperature of the black body and σ = 5.67 × 10-8 W/m2K4 is known as Stefan’s constant. A nuclear weapon may be thought of as a ball of radius 0.5 m. When denoted, it reaches temperature of 106K and can be treated as a black body.
a) estimate the power it radiates b) if surrounding has water at 30oC, how much water can 10% of the energy produced evaporate in 1 sec? Answer: a) We know that the expression for the power radiated...
A thin rod having length Lo at 0 degrees C and coefficient of linear expansion α has its two ends maintained at temperatures θ1 and θ2, respectively. Find its new length. Answer: Consider the following diagram
Answer: Consider the following diagram: From the diagram, this much can be said that: $ \theta =\frac{{{\theta }_{1}}+{{\theta }_{2}}}{2} $ The temperature changes in a linear fashion from θ1 to...
A rail track made of steel having length 10 m is clamped on a railway line at its two ends. On a summer day due to rise in temperature by 20oC, it is deformed as shown in the figure. Find x if αsteel = 1.2 × 10-5/oC.
Answer: According to the question, we have - αsteel = 1.2 × 10-5/oC and Lo = 10 m ∆T = 20oC Making use of the Pythagoras theorem, we have; $ {{x}^{2}}={{\left[ \frac{1}{2}(L+\Delta L)...
Calculate the stress developed inside a tooth cavity filled with copper when hot tea at a temperature of 57oC is drunk. You can take body temperature to be 37oC and α = 1.7 × 10-5oC, bulk modulus for copper = 140 × 109 N/m2.
Answer: According to the question, decrease in temperature is as follows: ∆t = 57 – 37 = 20oC The coefficient of linear expansion is as follows: α = 1.7 × 10-5oC And the bulk modulus for copper is:...
We would like to make a vessel whose volume does not change with temperature. We can use brass and iron (βbrass = 6 × 10-6/K and βiron = 3.55 × 10-5/K) to create a volume of 100 cc. How do you think you can achieve this?
Answer: According to the question, the volume of vessel is V = 100 cm3 = 10-4 = constant We also have that the volume of the iron vessel – Volume of brass rod = 10-4 m3 We know that: $ {{\beta...
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 would change in such a way that difference between their lengths remain constant. If αiron = 1.2 × 10-5/K and αbrass = 1.8 × 10-5/K, what should we take as length of each strip?
Answer: Change in length of iron rod is given as follows: $ \Delta L={{\alpha }_{iron}}{{L}_{iron}}\Delta T $ Change in length of brass rod is given as follows: $ \Delta L={{\alpha...
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 to bring mixture to a comfortable temperature. Suddenly Ramesh had to attend something which would take some times, say 5-10 minutes before he could take bath. Now he has two options:
a) fill the remaining bucket completely by cold water and then attend the work b) first attend to the work and fill the remaining bucket just before taking bath. Which option do you think would have...
100 g of water is supercooled to -10 degrees 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?
Answer: According to the question, the mass of water is 100 g At -10 degrees Celsius, the mixture has water and ice The expression for the heat required by the mixture is as follows: ms∆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 P-T diagram of water.
Answer: The graph above depicts the relationship between water pressure and temperature. When the pressure is increased, the ice becomes liquid, and when the pressure is decreased, it becomes solid....
Find out the increase in moment of inertia I of a uniform rod about its perpendicular bisector when its temperature is slightly increased by ∆T.
Answer: The picture above depicts a rod with a uniform mass M and a length l that is bisected perpendicularly. $ I=\frac{1}{12}M{{l}^{2}} $ When the temperature is raised, the rod length increases...
These days people use steel utensils 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.
Answer: Copper bottom utensils are utilised because, when compared to steel, copper is a better heat conductor. As a result, copper-bottomed utensils are utilised, and heat is distributed evenly....
Calculate the temperature which has same numerical value on Celsius and Fahrenheit scale.
Answer: For the construction of the temperature scale, consider two fixed points. The lower fixed point is the initial fixed point, which is for the freezing point. The upper fixed point is the...
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.
Answer: Because the rate of heat transfer through metal is faster than in wood, a metal bar seems to be hotter than a hardwood bar at the same temperature. Similarly, a metal bar appears to be...
A student records the initial length l, change in temperature ∆T and change in length ∆l of a rod as follows:
Sl.no l (m) ∆T (oC) ∆l (m) 1 2 10 4 × 10-4 2 1 10 4 × 10-4 3 2 20 2 × 10-4 4 3 10 6 × 10-4 If the first observation is correct, what can you say about observations 2, 3, and 4. Answer: Assume that...
Is the bulb of a thermometer made of diathermic or adiabatic wall?
Answer: A thermometer's bulb is made of diathermic walls, which allow heat to pass through. The bulb of a thermometer is built of diathermic walls, which enable heat energy to be exchanged between...
A glass full of hot milk is poured on the table. It begins to cool gradually. Which of the following is correct?
a) the rate of cooling is constant till milk attains the temperature of the surrounding b) the temperature of milk falls off exponentially with time c) while cooling, there is a flow of heat from...
Refer to the plot of temperature versus time showing the changes in the state of ice on heating. Which of the following is correct?
a) the region AB represents ice and water in thermal equilibrium b) at B water starts boiling c) at C all the water gets converted into steam d) C to D represents water and steam in equilibrium at...
‘Gulab Jamuns’ (assumed to be spherical) are to be heated in an oven. They are available in two sizes, one twice bigger than the other. Pizzas (assumed to be discs) are also to be heated in the oven. They are also in two sizes, one twice big in radius than the other. All four are put together to be heated to oven temperature. Choose the correct option from the following:
a) both size gulab jamuns will get heated at the same time b) smaller gulab jamuns are heated before bigger ones c) smaller pizzas are heated before bigger ones d) bigger pizzas are heated before...
Mark the correct options:
a) A system X is in thermal equilibrium with Y but not with Z. System Y and Z may be in thermal equilibrium with each other b) A system X is in thermal equilibrium with Y but not with Z. Systems Y...
A sphere, a cube, and a thin circular plate, all of the same material and same mass are initially heated to same high temperature.
a) plate will cool fastest and cube the slowest b) sphere will cool fastest and cube the slowest c) plate will cool fastest and sphere the slowest d) cube will cool fastest and plate the slowest...
The radius of a metal sphere at room temperature T is R, and the coefficient of linear expansion of the metal is α. The sphere is heated a little by a temperature ∆T so that its new Temperature is T + ∆T. The increase in the volume of the sphere is approximately
Answer: The correct option is d).
Heat is associated with
a) kinetic energy of random motion of molecules b) kinetic energy of orderly motion of molecules c) total kinetic energy of random and orderly motion of molecules d) kinetic energy of random motion...
As the temperature is increased, the time period of a pendulum
a) increases as its effective length increases even though its centre of mass still remains at the centre of the bob b) decreases as its effective length increases even though its centre of mass...
An aluminium sphere is dipped into water. Which of the following is true?
a) buoyancy will be less in water at 0oC than that in water at 4oC b) buoyancy will be more in the water at 0oC than that in water at 4oC c) buoyancy in water at 0oC will be same as that in the...
The graph between two temperature scales A and B is shown in the figure. Between upper fixed point and the 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
Answer: The correct answer is b)
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly
a) its speed of rotation increases b) its speed of rotation decreases c) its speed of rotation remains the same d) its speed increases because its moment of inertia increases Answer: The correct...
A bimetallic strip is made of aluminium and steel (αAl > αsteel). On heating, the strip will
a) remain straight b) get twisted c) will bend with aluminium on the concave side d) will bend with steel on the concave side Answer: The correct option is d) will bend with steel on the concave...
The triple points of neon and carbon dioxide are 24.57 K and 216.55 K, respectively. Express these temperatures on the Celsius and Fahrenheit scales.
Solution: Given: Kelvin and Celsius scales are related as: $\mathrm{T}_{\mathrm{C}}=\mathrm{T}_{\mathrm{K}}-273.15 \ldots . \ldots . \ldots . \ldots(1)$ We know that,...