Physics Exam Review: Gravity, Fluids, and Motion – Step-by-Step Study Guidance

Q1. Atmospheric pressure is caused by the: (i) density of the atmosphere; (ii) weight of the atmosphere; (iii) temperature of the atmosphere; (iv) solar energy on the atmosphere.

Background

Topic: Atmospheric Pressure

This question tests your understanding of what creates atmospheric pressure and the physical principles behind it.

Key Terms and Concepts:

• Atmospheric Pressure: The force per unit area exerted by the weight of the air above a surface.

• Density: Mass per unit volume of air.

• Weight: The force due to gravity acting on the mass of the atmosphere.

Step-by-Step Guidance

1. Recall that atmospheric pressure at a given point is due to the weight of the air column above that point.

2. Think about how the density and temperature of the atmosphere might affect the pressure, and whether they are direct causes or influencing factors.

3. Consider the role of gravity in holding the atmosphere to Earth and how this relates to pressure at the surface.

4. Evaluate each option and decide which is the most direct cause of atmospheric pressure.

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Q2. The principle of continuity states that for fluid flow to be continuous it must: (i) have no regions of stagnation; (ii) slow down in wide regions of flow; (iii) speed up in narrow regions of flow; (iv) both (ii) and (iii); (v) neither of these.

Background

Topic: Fluid Dynamics – Equation of Continuity

This question tests your understanding of how the speed of a fluid changes as it moves through regions of different cross-sectional area.

Key Terms and Formula:

• Equation of Continuity: For incompressible fluids, $A_1 v_1 = A_2 v_2$

• $A$ = cross-sectional area, $v$ = fluid velocity

Step-by-Step Guidance

1. Recall the equation of continuity and what it implies about the relationship between area and velocity in a pipe or channel.

2. Think about what happens to the velocity when the area decreases (narrow region) or increases (wide region).

3. Apply this reasoning to the options given and determine which statements are correct.

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Q3. As a balloon high in the atmosphere descends, it undergoes a decrease in: (i) volume; (ii) pressure; (iii) weight; (iv) density; (v) none of these.

Background

Topic: Gas Laws and Atmospheric Pressure

This question tests your understanding of how pressure and volume change for a gas (like a balloon) as it moves to lower altitudes.

Key Terms and Formula:

• Boyle's Law: $P_1 V_1 = P_2 V_2$ (for constant temperature)

• Atmospheric Pressure: Increases as you descend in the atmosphere.

Step-by-Step Guidance

1. Consider what happens to the external pressure on the balloon as it descends (goes lower in the atmosphere).

2. Recall how a change in external pressure affects the volume of a gas-filled balloon (Boyle's Law).

3. Think about whether the weight or density of the balloon changes significantly during descent.

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Q4. The barometer in the figure is used to measure the atmospheric pressure. If $h = 76$ cm, $\rho_{Hg} = 13.6$ g/cm$^3$, and $g = 9.8$ m/s$^2$, what is the height of mercury column?

Background

Topic: Fluid Statics – Barometric Pressure

This question tests your ability to use the hydrostatic pressure formula to relate the height of a mercury column to atmospheric pressure.

Key Formula:

• $P = \rho g h$

• $P$ = pressure, $\rho$ = density, $g$ = acceleration due to gravity, $h$ = height of column

Step-by-Step Guidance

1. Identify the known values: $h = 76$ cm, $\rho_{Hg} = 13.6$ g/cm$^3$, $g = 9.8$ m/s$^2$.

2. Convert all units to SI units if necessary (e.g., cm to m, g/cm$^3$ to kg/m$^3$).

3. Plug the values into the hydrostatic pressure formula $P = \rho g h$ to find the atmospheric pressure.

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Q5. In the figure below, which pressure is the highest? Apply Bernoulli's equation. (i) P1; (ii) P2; (iii) both are the same.

Background

Topic: Fluid Dynamics – Bernoulli's Principle

This question tests your understanding of how pressure and velocity are related in a moving fluid, as described by Bernoulli's equation.

Key Formula:

• Bernoulli's Equation: $P + \frac{1}{2} \rho v^2 + \rho g h = \text{constant}$

• $P$ = pressure, $\rho$ = density, $v$ = velocity, $h$ = height

Step-by-Step Guidance

1. Identify the two points in the diagram and note the relative velocities at each point.

2. Recall that, according to Bernoulli's equation, an increase in velocity leads to a decrease in pressure (if height is constant).

3. Compare the velocities at P1 and P2 to determine which has the higher pressure.

Try solving on your own before revealing the answer!