ऊष्मागतिकी, ऊर्जा एवं यांत्रिकी

An LVDT (Linear Variable Differential Transformer) is an inductive passive transducer used for measuring linear displacement by converting mechanical motion of a core into a proportional differential AC voltage signal. Option analysis: (A) Voltage is measured by voltmeters. (B) Current is measured by ammeters. (C) Displacement is the primary physical quantity measured by LVDT. (D) Temperature is measured by thermocouples, RTDs, or thermistors.

In agricultural and mechanical testing, seismic accelerometers (piezoelectric/piezoresistive) are standard transducers used to measure mechanical vibration (amplitude and frequency of oscillatory motion) on tractor seats, engines, and machine frames. (According to official answer key, option 2 'Vibration' is designated). Option analysis: (A) Speed is measured by tachometers/speedometers. (B) Vibration is the official key answer. (C) Acceleration is the physical parameter, but vibration is the application/official key. (D) Force is measured by load cells.

The theoretical power available in the wind stream through a rotor swept area

\(A = \frac{\pi d^2}{4}\) is given by: \[ P_a = \frac{1}{2} \rho A v^3 = \frac{1}{2} \rho \left(\frac{\pi d^2}{4}\right) v^3 \propto d^2 v^3 \]

If diameter

\(d' = 2d\) and wind speed \(v' = \frac{v}{2}\): \[ P'_a \propto (2d)^2 \left(\frac{v}{2}\right)^3 = 4d^2 \times \frac{v^3}{8} = \frac{4}{8} (d^2 v^3) = \frac{1}{2} P_a \]