JAMB 2022 Physics · Question 15

A reservoir is filled with liquid of density 2000 kgm ^ -1 . Calculate the depth at which the pressure in the…

Question

A reservoir is filled with liquid of density 2000 kgm $^{-1}$ . Calculate the depth at which the pressure in the liquid will be equal to 9100 Nm $^{-2}$ (g = 10 ms $^{-2}$ )

A.0.262 m
B.0.664 m
C.0.819 m
D.0.455 m

Answer: D. 0.455 m

Explanation written with AI and checked against the answer key

Analyze the question: We need the depth h at which the liquid pressure is 9100 N/m². The density is 2000 kg/m³ (the "kgm⁻¹" in the question is a typo for kgm⁻³), and g = 10 m/s². Concept: Pressure due to a liquid column is P = ρgh, so h = P / (ρg) Solution: h = 9100 / (2000 × 10) h = 9100 / 20000 h = 0.455 m Answer: The depth is 0.455 m, which is option D. Note: this treats 9100 N/m² as the pressure due to the liquid alone. If atmospheric pressure were added, the pressure would be far larger than 9100 N/m² (atmospheric pressure is about 100,000 N/m²), so the question clearly means the liquid pressure only. Tip: In JAMB calculation questions, check the units first. A typo like "kgm⁻¹" is common, so read it as the standard density unit kgm⁻³. Then rearrange the formula before substituting: h = P/(ρg). Also, 9100/20000 is easy to do quickly: 9100/2 = 4550, then divide by 10,000 to get 0.455.

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