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Explanation: Newton’s law states that gravitational force (F) is directly proportional to the product of the masses (M × m) of two objects and inversely proportional to the square of the distance (d) between their centers, expressed as F = G × (M × m) / d².
Explanation: The standard value of gravitational acceleration on Earth’s surface is approximately 9.8 meters per second squared.
Explanation: Using the formula F = m × g, where m = 10 kg and g = 9.8 m/s², the gravitational force is 10 × 9.8 = 98 Newtons.
Explanation: An iceberg floats because its density is less than that of water, allowing it to displace enough water to balance its weight.
Explanation: In free fall, the only force acting on the object is gravity, causing it to accelerate at a rate of g, approximately 9.8 m/s².
Explanation: The gravitational force is inversely proportional to the square of the distance between the objects. If the distance is halved, the force increases by a factor of 2² = 4.
Explanation: The weight of an object on the Moon is less because the Moon's mass is significantly smaller than Earth's, resulting in a weaker gravitational pull. The gravitational acceleration on the Moon is about 1/6th of that on Earth.
Explanation: This formula represents Newton’s Universal Law of Gravitation, where F is the gravitational force, G is the gravitational constant, M and m are the masses of the two objects, and d is the distance between them.
Explanation: Using the equation for uniformly accelerated motion, v² = u² + 2as, where v = 0 at maximum height, u = 49 m/s, and a = -g (acceleration due to gravity = -9.8 m/s²), we get 0 = 49² - 2 × 9.8 × s. Solving for s gives s = 122.5 meters.
Explanation: According to Archimedes' principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Explanation: Since gravitational force is inversely proportional to the square of the distance, doubling the force would require the distance to be reduced by a factor of √2.
Explanation: Gravitational force is inversely proportional to the square of the distance. Tripling the distance reduces the force by a factor of 3² = 9.
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