Question

If a coin at the bottom of a lake appears to be at a depth of $6,m$, then the gauge pressure on the coin in pascal is ($\mu$ of water = $\frac{4}{3}$)

• A. $8.2\times10^3$
• B. $78.4\times10^3$
• C. $38.2\times10^3$
• D. $4.5\times10^4$
• E. $29.4\times10^3$

Hint:

Physics Tip: Objects under water always appear raised. Real depth = $\mu \times$ apparent depth.

Answer 1

The Correct Option is B

Concept:
For viewing an object inside water from air: $$\text{Apparent depth}=\frac{\text{Real depth}}{\mu}$$ Also, gauge pressure at depth $h$: $$P=\rho gh$$
Step 1: Find real depth.
Given: $$\text{Apparent depth}=6m,\quad \mu=\frac{4}{3}$$ So, $$6=\frac{h}{4/3}$$ $$h=6\times\frac{4}{3}=8m$$
Step 2: Calculate gauge pressure.
For water: $$\rho=1000,kg/m^3,\quad g=9.8,m/s^2$$ $$P=\rho gh=1000\times9.8\times8$$ $$=78400,Pa$$ $$=78.4\times10^3,Pa$$
Step 3: Final answer.
Hence correct option is (B). :contentReference[oaicite:0]{index=0}