1. Problem Statement: (i) Describe the working principle of pressure gauges with a diagram. (ii) Calculate the deflection of a Bourdon tube given $r=50$ mm, $E=210$ GPa, $t=0.5$ mm, and pressure $p=200$ kPa. (iii) Describe an experiment to investigate the photoelectric effect as an example of a radiation transducer. 2. Working Principle of Pressure Gauges: Pressure gauges measure fluid pressure by converting pressure into mechanical displacement. A common type is the Bourdon tube gauge, which uses a curved tube that tends to straighten when internal pressure increases. This mechanical movement is linked to a pointer indicating pressure on a dial. 3. Bourdon Tube Deflection Calculation: The deflection $\\delta$ of a Bourdon tube under pressure $p$ is given by: $$\\delta = \\frac{3 p r^2}{E t}$$ where: - $p$ = internal pressure - $r$ = initial radius of curvature - $E$ = Young's modulus - $t$ = tube thickness Given: $p = 200$ kPa = $200 \\times 10^3$ Pa $r = 50$ mm = 0.05 m $E = 210$ GPa = $210 \\times 10^9$ Pa $t = 0.5$ mm = 0.0005 m Calculate: $$\\delta = \\frac{3 \\times 200 \\times 10^3 \\times (0.05)^2}{210 \\times 10^9 \\times 0.0005}$$ $$= \\frac{3 \\times 200 \\times 10^3 \\times 0.0025}{105 \\times 10^6}$$ $$= \\frac{1500}{105 \\times 10^6} = 1.4286 \\times 10^{-5} \, m = 14.29 \, \\mu m$$ 4. Photoelectric Effect Experiment: - Shine monochromatic light of known frequency on a clean metal surface inside a vacuum tube. - Connect the metal to an adjustable voltage circuit and measure the current of emitted electrons. - Vary the frequency and intensity of light and record the stopping voltage where current ceases. - Observe that electrons are emitted only above a threshold frequency, confirming the quantum nature of light. - This experiment demonstrates conversion of radiation energy into electrical energy, characteristic of a radiation transducer. Final answers: - Deflection of Bourdon tube: $14.29 \, \\mu m$