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.
Derive the expression for the electric field on the axial and equatorial lines of an electric dipole at a point in space.
Read the paragraph and answer the questions following it.
Water is essential for life. Without water there would be no life.
We usually take water as granted for its purity, but we must
ensure the quality of water. Pollution of water originates from
human activities. Through different paths, pollution reaches to
ground water. Easily identified source or place of pollution is
called as point source, e.g.– municipal and industrial discharge
pipes, where pollutants enter the water source. Non–point sources
of pollution are those where a source of pollution can not be
easily identified, e.g.– agricultural run off, acid rain etc.
(i) How do you classify the various sources of water pollution?
(ii) What are the point sources of water pollution?
(iii) Name any two non-point sources of water pollution?
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