Explain the Doppler effect in sound and derive the formula for the observed frequency when the source is moving towards a stationary observer. Calculate the observed frequency if the source frequency is 500 Hz and the source moves towards the observer at 30 m/s. (Speed of sound = 340 m/s)
Explain the first law of thermodynamics and describe an isothermal process. Calculate the work done during an isothermal expansion if 2 moles of an ideal gas expand from 1 liter to 5 liters at 300 K.
State Kepler’s laws of planetary motion. Derive the expression for the orbital speed of a satellite around Earth using Newton’s law of gravitation.
A block of mass 5 kg is placed on a horizontal surface with a coefficient of friction of 0.4. Calculate the minimum force required to move the block and the acceleration if the applied force is 50 N. (g = 9.8 m/s²)
Derive the formula for the maximum height and range of a projectile launched at an angle θ with initial velocity u. Calculate the range if u = 20 m/s and θ = 45°.
State Lenz’s Law. A coil is moved towards a stationary bar magnet. Explain how Lenz’s law helps determine the direction of the induced current in the coil.
Derive the lens formula (1/f = 1/v – 1/u) for a convex lens and explain how magnification is affected if the object distance is changed.
A proton moves at a speed of 2 x 10^6 m/s perpendicular to a magnetic field of 1 T. Calculate the force acting on the proton and its radius of the circular path. (Charge of proton = 1.6 x 10^-19 C)
A wire has a resistance of 10 ohms at room temperature. Explain what happens to the resistance of the wire if (a) the wire is heated, and (b) the length of the wire is doubled while keeping its volume constant.
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