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Derive the expression for centripetal acceleration.
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Calculate the average velocity of the particle whose position vector changes from `vecr_1 = 5hati + 6hatj` to `vecr_2 = 2hati + 3hatj` in a time 5 second.
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The following table gives the range of a particle when thrown on different planets. All the particles are thrown at the same angle with the horizontal and with the same initial speed. Arrange the planets in ascending order according to their acceleration due to gravity, (g value).
| Planet | Range |
| Jupiter | 50 m |
| Earth | 75 m |
| Mars | 90 m |
| Mercury | 95m |
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The following graphs represent the velocity-time graph. Identify what kind of motion a particle undergoes in each graph.
| (a) | ![]() |
| (b) | |
| (c) | ![]() |
| (d) | ![]() |
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An ideal refrigerator has a freezer at a temperature of −12°C. The coefficient of performance of the engine is 5. The temperature of the air (to which the heat ejected) is ____________.
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Define the coefficient of performance.
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Explain in detail the working of a refrigerator.
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An ideal refrigerator keeps its content at 0°C while the room temperature is 27°C. Calculate its coefficient of performance.
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A container has one mole of the monoatomic ideal gas. Each molecule has f degrees of freedom. What is the ratio of γ = `"C"_"p"/"C"_"v"`?
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A sample of gas consists of μ1 moles of monoatomic molecules, μ2 moles of diatomic molecules and μ3 moles of linear triatomic molecules. The gas is kept at a high temperature. What is the total number of degrees of freedom?
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Define the term degrees of freedom.
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An air column in a pipe which is closed at one end, will be in resonance with the vibrating body of frequency 83Hz. Then the length of the air column is ______.
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Consider two uniform wires vibrating simultaneously in their fundamental notes. The tensions, densities, lengths and diameter of the two wires are in the ratio 8 : 1, 1 : 2, x : y and 4 : 1 respectively. If the note of the higher pitch has a frequency of 360 Hz and the number of beats produced per second is 10, then the value of x : y is
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What is meant by end correction in resonance air column apparatus?
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Describe the total degrees of freedom for monoatomic molecule, diatomic molecule and triatomic molecule.
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How will you determine the velocity of sound using resonance air column apparatus?
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Derive the ratio of two specific heat capacities of monoatomic, diatomic and triatomic molecules.
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During an adiabatic process, the pressure of a mixture of monatomic and diatomic gases is found to be proportional to the cube of the temperature. Find the value of γ = `("C"_"P"/"C"_"V")`
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A gas made of a mixture of 2 moles of oxygen and 4 moles of argon at temperature T. Calculate the energy of the gas in terms of RT. Neglect the vibrational modes.
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