How do a scalar quantity and a vector quantity differ?

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HESI A2

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Question 1 of 5

How do a scalar quantity and a vector quantity differ?

Correct Answer: C

Rationale: The correct answer is C. The main difference between a scalar quantity and a vector quantity lies in the presence of direction. A vector quantity has both magnitude and direction, while a scalar quantity has magnitude only, without any specified direction. Examples of scalar quantities include distance, speed, temperature, and energy, whereas examples of vector quantities include displacement, velocity, force, and acceleration. Choices A, B, and D are incorrect because they incorrectly describe the characteristics of scalar and vector quantities.

Question 2 of 5

Two objects attract each other with a gravitational force of 12 units. If you double the distance between the objects, what is the new force of attraction between the two?

Correct Answer: A

Rationale: The gravitational force between two objects is inversely proportional to the square of the distance between them. If the distance is doubled, the force will be reduced to 1/4 of the original force. Therefore, the new force of attraction between the two objects will be 12 units / 4 = 3 units. Choice A is correct because doubling the distance reduces the force to 1/4 of the original value. Choices B, C, and D are incorrect as they do not consider the inverse square relationship between distance and gravitational force.

Question 3 of 5

What is the purpose of a switch in a circuit?

Correct Answer: D

Rationale: The purpose of a switch in a circuit is to allow the circuit to open and close. When the switch is turned on, it provides a complete path for the current to flow through the circuit. When the switch is turned off, it breaks the circuit, stopping the flow of current. This function of opening and closing the circuit using a switch is essential for controlling the flow of electricity in various electrical devices and systems. Choices A, B, and C are incorrect because a switch does not reverse the direction of current, increase voltage, or increase resistance in a circuit; its primary function is to open and close the circuit.

Question 4 of 5

When a car is driven for a long time, the pressure of air in the tires increases. This is best explained by which of the following gas laws?

Correct Answer: C

Rationale: Gay-Lussac's law, also known as the law of pressure-temperature, states that the pressure of a gas is directly proportional to its absolute temperature when the volume is constant. As a car is driven for a long time, the tires heat up due to friction and increased air pressure inside the tires. This results in an increase in temperature, causing the pressure of the air inside the tires to increase according to Gay-Lussac's law. Choices A, B, and D are incorrect. Boyle's law relates pressure and volume, Charles' law relates volume and temperature, and Dalton's law deals with the partial pressures of gases in a mixture.

Question 5 of 5

A 5-cm candle is placed 20 cm away from a concave mirror with a focal length of 15 cm. About what is the image height of the candle in the mirror?

Correct Answer: B

Rationale: The magnification formula for a mirror is given by M = -f / (f - d), where f is the focal length of the mirror, and d is the object distance from the mirror. Using the mirror equation and magnification formula, the image height is found to be negative because it is inverted. Plugging in the values (f = 15 cm, d = 20 cm) into the formula gives M = -15 / (15 - 20) = -15 / -5 = 3. The negative sign indicates that the image is inverted. The image height is then calculated by multiplying the magnification by the object height: 3 * 5 cm = 15 cm. Therefore, the correct image height is approximately -15 cm. Choice A (30.5 cm) and Choice D (-30.5 cm) are incorrect as they do not consider the inversion of the image. Choice C (-15 cm) is also incorrect because it neglects the negative sign, which indicates the inversion of the image.

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