Question
On the basis of molecular kinetic theory derive an expression for the pressure exerted on the walls of a vessel by a gas filled in it.
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Suppose the smaller pulley of the previous problem has its radius $5.0cm$ and moment of inertia $0.10kg-m^2$. Find the tension in the part of the string joining the pulleys.
→Consider an ideal gas with following distribution of speeds.
Calculate $V_{rms}$ and hence T. $(m = 3.0 \times 10^{-26}kg)$
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Speed m/s
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200
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400
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600
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800
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1000
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% of molecules
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10
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20
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40
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20
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10
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What are beats? Prove that the number of beats produced per second by the two sound sources is equal to the difference between their frequencies.
Some equipotential surfaces are shown in figure. What can you say about the magnitude and the direction of the electric field?
An air chamber of volume V has a neck area of cross section a into which a ball of mass m just fits and can move up and down without any friction (Fig.). Show that when the ball is pressed down a little and released , it executes SHM. Obtain an expression for the time period of oscillations assuming pressure-volume variations of air to be isothermal [see Fig.].
A square loop PQRS carrying a current of 6.0A is placed near a long wire carrying 10A as shown in figure.
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- Find the magnetic force on the square loop.
The potentiometer wire AB shown in figure. is 50cm long. When AD = 30cm, no deflection occurs in the galvanometer. Find R.
A geyser heats water flowing at the rate of $3.0$ litres per minute from $27°C$ to $77°C$. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is $4.0 × 104J/g$?
→The transverse displacement of a string (clamped at its both ends) is given by
$\text{y}(\text{x, t})=0.06\sin\Big(\frac{2\pi}{3}\text{x}\Big)\cos(120\pi\text{ t})$
where x and y are in m and t in s. The length of the string is $1.5m$ and its mass is $3.0 \times 10^{–2}kg$.
Answer the following:
Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency, and speed of each wave?
→$\text{y}(\text{x, t})=0.06\sin\Big(\frac{2\pi}{3}\text{x}\Big)\cos(120\pi\text{ t})$
where x and y are in m and t in s. The length of the string is $1.5m$ and its mass is $3.0 \times 10^{–2}kg$.
Answer the following:
Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency, and speed of each wave?
Use the formula $\text{v}=\sqrt{\frac{\gamma\text{P}}{\rho}}$ to explain why the speed of sound in air:
Increases with temperature,
→Increases with temperature,