Q101 / 150 · MHT CET 2026 (17 April Shift 2) · Physics
A force 'F' is applied on a square plate of side 'L'. If the percentage error in determining 'L' is 3% and that in 'F' is 2% then the percentage error in determining the pressure is
- A$5\%$
- B$6\%$
- C$7\%$
- Correct answerD$8\%$
Solution
Pressure is given by $P = \dfrac{F}{A}$
For a square plate of side $L$, the area is $A = L^2$
Therefore, $P = \dfrac{F}{L^2}$
The maximum percentage error in pressure is given by $\dfrac{\Delta P}{P} \times 100 = \dfrac{\Delta F}{F} \times 100 + 2 \left( \dfrac{\Delta L}{L} \times 100 \right)$
Given $\dfrac{\Delta F}{F} \times 100 = 2\%$ and $\dfrac{\Delta L}{L} \times 100 = 3\%$
Substituting the values, we get $\dfrac{\Delta P}{P} \times 100 = 2\% + 2(3\%) = 8\%$
Answer: $8\%$
For a square plate of side $L$, the area is $A = L^2$
Therefore, $P = \dfrac{F}{L^2}$
The maximum percentage error in pressure is given by $\dfrac{\Delta P}{P} \times 100 = \dfrac{\Delta F}{F} \times 100 + 2 \left( \dfrac{\Delta L}{L} \times 100 \right)$
Given $\dfrac{\Delta F}{F} \times 100 = 2\%$ and $\dfrac{\Delta L}{L} \times 100 = 3\%$
Substituting the values, we get $\dfrac{\Delta P}{P} \times 100 = 2\% + 2(3\%) = 8\%$
Answer: $8\%$
Hence, the correct answer is option: 'D'.