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The specific heat capacity of water is about 2 J/g°C. How much energy would you need to heat 1 kilogram of water by 10°C?
- A. 420 J
- B. 4,200 J
- C. 42,000 J
- D. 420,000 J
Correct Answer: C
Rationale: The formula to calculate the energy required to heat a substance is Q = m c ΔT, where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Given that 1 kilogram of water is equal to 1,000 grams, the mass (m) is 1,000 g, the specific heat capacity (c) of water is 4.2 J/g°C (not 2 J/g°C), and the change in temperature (ΔT) is 10°C. Substituting these values into the formula: Q = 1,000 4.2 10 = 42,000 J. Therefore, the correct energy required to heat 1 kilogram of water by 10°C is 42,000 J. Choices A, B, and D are incorrect as they do not consider the correct specific heat capacity of water or the conversion of mass to grams.
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As a car is traveling on the highway, its speed drops from 60 mph to 30 mph. What happens to its kinetic energy?
- A. Its energy is halved.
- B. Its energy is doubled.
- C. Its energy is quadrupled.
- D. Its energy is divided by four.
Correct Answer: A
Rationale: The correct answer is A. Kinetic energy is proportional to the square of the velocity. When the speed drops from 60 mph to 30 mph, the kinetic energy is halved. Choice B is incorrect because halving the speed results in halving the kinetic energy, not doubling it. Choice C is incorrect because quadrupling the kinetic energy would require increasing the speed fourfold, not halving it. Choice D is incorrect because dividing the energy by four would imply a different relationship between speed and kinetic energy, which is not the case.
A rock has a volume of 6 cm3 and a mass of 24 g. What is its density?
- A. 4 g/cm3
- B. 4 cm3/g
- C. 144 g/cm3
- D. 144 cm3/g
Correct Answer: A
Rationale: Density is calculated by dividing the mass of an object by its volume. In this case, the mass of the rock is 24 g and its volume is 6 cm3. By dividing 24 g by 6 cm3, we find that the density of the rock is 4 g/cm3. Choice A is the correct answer because density is expressed in units of mass per unit volume (g/cm3). Choice B is incorrect as it represents the reciprocal of density. Choices C and D are significantly higher values and do not match the calculated density of the rock.
Which mathematical quantity is scalar?
- A. Distance
- B. Velocity
- C. Acceleration
- D. Displacement
Correct Answer: A
Rationale: Distance is a scalar quantity because it has only magnitude and no direction. It is simply the total length of the path travelled by an object. Scalars are quantities that are fully described by their magnitude alone, without any reference to direction. Velocity and acceleration are vector quantities as they have both magnitude and direction. Displacement is also a vector quantity as it is the change in position of an object and includes both magnitude and direction.
Power (P) represents the rate of work done. Which formula accurately depicts power?
- A. P = W / F
- B. P = d / t
- C. P = W x t
- D. P = F / t
Correct Answer: D
Rationale: Power (P) is defined as the rate of work done over time. The correct formula for power is P = W/t, where W is the work done, and t is the time taken. Therefore, option D, P = F / t, correctly represents power as work divided by time. Option A, P = W / F, is incorrect as it represents work divided by force, not power. Option B, P = d / t, is incorrect as it represents distance divided by time, not power. Option C, P = W x t, is incorrect as it represents work multiplied by time, not power. It's important to understand the distinction between work, power, force, time, and other related concepts to solve physics problems accurately.
An object with a mass of 45 kg has momentum equal to 180 kgâ‹…m/s. What is the object's velocity?
- A. 4 m/s
- B. 8.1 km/s
- C. 17.4 km/h
- D. 135 m/s
Correct Answer: A
Rationale: The momentum of an object is calculated by multiplying its mass and velocity. Mathematically, momentum = mass x velocity. Given that the mass is 45 kg and the momentum is 180 kgâ‹…m/s, we can rearrange the formula to solve for velocity: velocity = momentum / mass. Plugging in the values, velocity = 180 kgâ‹…m/s / 45 kg = 4 m/s. Therefore, the object's velocity is 4 m/s. Choices B, C, and D are incorrect because they do not align with the correct calculation based on the given mass and momentum values.