The pressure on a square plate is measured by measuring the force acting on the plate and length of the sides of the plate. The maximum error in the measurement of force and length are respectively 4\% and 2\%, the percentage error in the measurement of pressure is

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Examsnet · Accepted Answer

Correct Answer is : 8%8\%8%Step 1: FormulaPressure:P=FAP=F/AP=AF​For a square plate of side LLL :A=L2,P=FL2A=L², P={F}{L²}A=L2,P=L2F​Step 2: Error propagationFor quantities with powers, percentage (relative) errors add with exponents in absolute value:ΔPP=ΔFF+2ΔLLΔ P/P=Δ F/F+2 Δ L/LPΔP​=FΔF​+2LΔL​Step 3: Substitute given errors[-] Error in FFF: 4%4\%4%[-] Error in LLL: 2%2\%2%So:%\%% error inP=4%+2×2%=4%+4%=8%P=4\%+2 × 2\%=4\%+4\%=8\%P=4%+2×2%=4%+4%=8%✓ Final Answer:Option D: 8%8\%8%

MHTCET 23 Apr 2025 Shift 2 Paper