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

Correct Answer: C

Rationale: The gravitational force between two objects is directly proportional to the product of their masses. When you double the masses of both objects, the force of attraction between them increases by a factor of 2 x 2 = 4. Therefore, the new force of attraction between the two objects will be 12 units x 4 = 24 units. Choices A, B, and D are incorrect because doubling the mass results in a quadruple increase in force, not a linear one.

Correct Answer: B

Rationale: The relationship between acceleration and force is expressed in Newton's second law of motion. This law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object's mass. Mathematically, this relationship is represented as F = ma, where F is the force, m is the mass of the object, and a is the acceleration. Choice A, Newton's first law of motion, also known as the law of inertia, states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an external force. Choice C, Newton's third law of motion, states that for every action, there is an equal and opposite reaction, focusing on the interaction between two objects. Choice D is incorrect because the relationship between acceleration and force is indeed described by one of Newton's laws of motion, specifically the second law.

Correct Answer: C

Rationale: To find the image distance of the candle, we use the mirror formula: 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. In this case, the focal length f = 10 cm and the object distance do = 20 cm. Substituting these values into the formula gives us 1/10 = 1/20 + 1/di. Solving for di, we get di = 60 cm. Therefore, the image distance of the candle is 60 cm. Choice A (20 cm) is incorrect because it represents the object distance, not the image distance. Choice B (40 cm) is incorrect as it does not consider the mirror formula calculation. Choice D (75 cm) is incorrect as it does not match the correct calculation based on the mirror formula.

Correct Answer: B

Rationale: The frequency of a wave is calculated using the formula: frequency = speed / wavelength. In this case, the speed of the wave is 12 m/s and the wavelength is 2 m. Therefore, the frequency is calculated as 12 m/s / 2 m = 6 Hz. Choice A (38.4 Hz), Choice C (4.6 Hz), and Choice D (3.75 Hz) are incorrect as they do not result from the correct calculation using the given values.

Correct Answer: D

Rationale: The momentum of an object is calculated by multiplying its mass by its velocity. The momentum formula is p = m v, where p is momentum, m is mass, and v is velocity. Comparing the momentum of each vehicle: A: 9,000 kg 3 m/s = 27,000 kg·m/s B: 2,000 kg 24 m/s = 48,000 kg·m/s C: 1,500 kg 29 m/s = 43,500 kg·m/s D: 500 kg 89 m/s = 44,500 kg·m/s. Therefore, the glider (500-kg) traveling at 89 m/s has the greatest momentum of 44,500 kg·m/s, making it the correct choice. Options A, B, and C have lower momentum values compared to option D, proving that the 500-kg glider traveling at 89 m/s has the highest momentum among the given vehicles.