Answered

3.
The height of mercury column of a barometer is 760 mm. Calculate the pres
sure exerted on the mercury column, if density of mercury is 13.6 gm/cm³
and acceleration due to gravity is 9.8 m/s².
(Ans: 1.013 x 10³ pa)

Verified Answer :

GinnyAnswer

Sure! Let's solve this problem step-by-step:

### Given:
- Height of mercury column, \(\( h = 760 \)\) mm
- Density of mercury, \(\( \rho = 13.6 \)\) gm/cm³
- Acceleration due to gravity, \(\( g = 9.8 \)\) m/s²

### Step 1: Convert the height from mm to meters
Since 1 mm is equal to 0.001 meters:
\(\[ h = 760 \, \text{mm} \times 0.001 \, \frac{\text{meters}}{\text{mm}} = 0.76 \, \text{m} \]\)

### Step 2: Convert the density from gm/cm³ to kg/m³
Since 1 gm/cm³ is equal to 1000 kg/m³:
\(\[ \rho = 13.6 \, \frac{\text{gm}}{\text{cm}^3} \times 1000 \, \frac{\text{kg}}{\text{m}^3 \, \frac{\text{gm}}{\text{cm}^3}} = 13600 \, \frac{\text{kg}}{\text{m}^3} \]\)

### Step 3: Calculate the pressure using the formula \(\( P = h \rho g \)\)
\(\[ P = h \times \rho \times g \]\)
\(\[ P = 0.76 \, \text{m} \times 13600 \, \frac{\text{kg}}{\text{m}^3} \times 9.8 \, \frac{\text{m}}{\text{s}^2} \]\)

### Step 4: Compute the final value:
\(\[ P = 0.76 \times 13600 \times 9.8 \]\)
\(\[ P = 101292.8 \, \text{Pa} \]\)

Therefore, the pressure exerted on the mercury column is \(\( 101292.8 \)\) Pascals, which can be approximated as \(\( 1.013 \times 10^5 \)\) Pascals.

Related Questions