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SECTION 'B' (Short-Answer Questions) (36)
NOTE: Answer any NINE part questions from this section. All questions carry equal marks. Draw diagrams where necessary. Use of scientific calculator is allowed. All notations are used in their usual meanings
2.
i) Prove that the following equations are dimensionally correct:
*T = 2π √(l/g)
*F = mv2/r
ii) What is angle of repose? Derive relation between angle of friction and angle of repose.
iii) State and prove work-energy equation/theorem.
iv) Derive equation of continuity.
v) At what angle the horizontal range of projectile become equal to its vertical range? Prove mathematically.
vi) A car has been sounding a 4k HZ tone. What frequency will be detected by a stationary listener as the car approaches him at 50 km/h? (speed of sound in air = 1200 km/h)
vii) A parallel plate capacitor consists of two plates with an area of 0.1 m2 each separated by 0.002 m. The capacitor is filled with dielectric material having relative permittivity εr = 4. Calculate the capacitance of the capacitor. (ε0 = 8.85 × 10-12 C2/N.m2)
viii) A tank 4 m long, 3 m wide and 2 m deep is filled to the brim with the paraffin of density = 800 kg/m3. Calculate the pressure on the base (g = 10 m/s2)
ix) A machine gun fires 10 bullets per second into a target. Each bullet weigh 30 gram and had a speed of 1500 m/s. Find the force necessary to hold the gun in its position.
x) A body of mass 5 gram oscillating as a simple pendulum. Calculate the time period of the pendulum, if its length is 1.2 m.
xi) What is meant by interference of light? Write three conditions of interference of light.
xii) Define Electric Flux. Prove that the net electric flux through a closed surface is equal to 1ε0 time the total charge enclosed in the surface.
xiii) A 20 meter length of cable has a cross-sectional area of 1 mm2 and a resistance of 5 ohms. Calculate the resistivity of the cable.
xiv) Calculate the value of one of the two equal charges if they repel one another with a force of 0.15 N, when situated 40 cm apart in a vacuum. (Coulomb's constant for vacuum is 9 × 109 N.m2/C2)
SECTION “C” (Detailed Answer Questions)(32)
NOTE: Attempt any TWO questions from this section. All questions carry equal marks. Draw diagrams where necessary.
3.
a) Define Projectile Motion. Derive mathematical equations for the following:
i) Time to reach maximum height
ii) Range of the projectile
b) Define Simple Harmonic Motion. A particle is moving in a circle with constant speed. Prove that its projection performs Simple Harmonic Motion (SHM) along one of the diameter of the circle.
4.
a) State and prove law of conservation of linear momentum.
b) Define capacitance of a capacitor. Derive mathematical relations for capacitance of parallel plate capacitor when;
(i) air is present between its plates
(ii) A dielectric slab is present between its plate
5.
a) What is diffraction of light? How a diffraction gating is used to determine the wavelength of monochromatic light. Derive the relevant mathematical expression.
b) Explain Newton's formula for the speed of sound in air. Why the speed of sound in air from Newton's formula was not in good agreement with the experimental value? How did Laplace correct it? Explain.
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