Pressure, barometer

Solution

Option (d) is correct.

Explanation:

where \( m = 2 \, \text{kg} \) (mass of the box) and \( g = 9.81 \, \text{m/s}^2 \) (acceleration due to gravity). Now calculate the weight \( F \): \[ F = 2 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 19.62 \, \text{N} \] The area \( A \) of the surface in contact with the table is given by: \[ A = 30 \, \text{cm} \times 10 \, \text{cm} = 300 \, \text{cm}^2 = 300 \times 10^{-4} \, \text{m}^2 = 0.03 \, \text{m}^2 \] Pressure \( P \) is calculated using: \[ P = \frac{F}{A} \] Substituting the values: \[ P = \frac{19.62 \, \text{N}}{0.03 \, \text{m}^2} = 654 \, \text{N/m}^2 \approx 666.6 \, \text{N/m}^2 \]

Correct Answer

📖 Governing Law / Core Concept

The pressure exerted at the base of a liquid column is given by:

Where: - \( P \) = pressure (Pa), - \( \rho \) = density of the liquid (kg/m³), - \( g \) = acceleration due to gravity (\(9.81 \, \text{m/s}^2\)), - \( h \) = height of the liquid column (m).

🧪 Step-by-Step Breakdown

According to the hydrostatic pressure equation:

From the equation, we see that:

- Pressure \( P \) is directly proportional to the height \( h \) of the liquid column. - The pressure does not depend on the area of the base of the beaker, which means smaller or larger base areas won't affect the pressure at the bottom.

🔍 Option Analysis

Option (a): Incorrect, as pressure is independent of area. Option (c): Incorrect, pressure does depend on density. Option (d): Incorrect, as pressure is directly proportional to height.

⚡ Mnemonic / Speed-Run

Remember: "Pressure Proportional to Height" - Just think \( P \propto h \).

6. Visual Suggestion

📖 Factual Verification & Reference

Correct Answer

📖 Governing Law / Core Concept

Pressure is defined as force per unit area, represented mathematically as: where \( P \) is pressure, \( F \) is force (in Newtons), and \( A \) is area (in square meters).

🧪 Step-by-Step Breakdown

Pressure is measured in Pascals (Pa) in SI units. 1 Pascal is defined as: Thus, Pascal and N/m² are directly equivalent, confirming that Option D is correct.

🔍 Option Analysis

• Option A: Incorrect; pressure is a scalar quantity, having only magnitude, not direction.
• Option B: Incorrect; pressure increases with depth in a liquid due to the weight of the liquid above.
• Option C: Incorrect; action and reaction forces (Newton's Third Law) act on different objects, not the same object.

⚡ Mnemonic / Speed-Run

Remember: Pressure is Force per Area (\( P = F/A \)) & 1 Pascal = 1 N/m².

📖 Factual Verification & Reference

Correct Answer

📖 Governing Law / Core Concept

The phenomenon of the twinkling of stars can be explained through the principles of atmospheric refraction. When starlight enters Earth’s atmosphere, it passes through layers of air with varying densities, leading to the bending of the light path.

🧪 Step-by-Step Breakdown

Light travels at different speeds in different mediums. The critical concepts include: - **Refraction Index**: \( n = \frac{c}{v} \) where \( n \) is the refractive index, \( c \) is the speed of light in vacuum, and \( v \) is the speed of light in the medium. - As starlight passes through various atmospheric layers, it is refracted, causing the apparent position of stars to shift slightly. This results in the perception of twinkling. \[ n = \frac{c}{v} \] The change in refractive index due to temperature variations at different altitudes leads to the continuous shifting of the light from the star, causing it to appear to twinkle.

🔍 Option Analysis

- **A: Particular frequencies of the starlight** - Incorrect, as twinkling is not related to frequency but to light bending. - **B: Reflection from the oceanic surface** - Incorrect, ocean reflections do not cause twinkling; they scatter light. - **D: Magnetic field of Earth** - Incorrect, as the magnetic field does not influence light from stars.

⚡ Mnemonic / Speed-Run

**Remember:** "Stars Twinkle Through Atmosphere" (STTA) to recall that twinkling is due to atmospheric conditions affecting light.

6. Visual Suggestion

📖 Factual Verification & Reference