Gravitation and Center of Mass

The Sun's mass is approximately 333,000 times that of Earth. This means you would need about 333,000 Earths to equal the Sun's mass. The option 330,000 is the closest approximation among the choices.

Gravity is the fundamental force that caused the early Earth to pull material together, forming a spherical shape. A sphere is the most stable shape under gravitational pull for a body of Earth's size.

Earth is spherical due to gravity, which pulls all matter toward the center of mass. During Earth's formation, the molten material was pulled equally inward in all directions by gravitational force, naturally forming a sphere (the shape with minimum surface area for a given volume. This is why all large bodies in space (planets, stars) are spherical. Magnetism attracts only certain materials, and heat would cause expansion, not spherical shaping.

The Earth's mass is approximately 5.97 x 10^24 kg, which is about 6.6 sextillion tons. This value can be written in scientific notation as 6.6 x 10^21 tons, matching the given figure when converted.

Assuming a uniform Earth density (ideal case), gravitational force inside the Earth is proportional to distance from center, exactly like a spring's restoring force. The coin accelerates toward the center, reaches maximum speed there, then decelerates, and returns - executing simple harmonic motion. Realistically, Earth's non-uniform density makes it approximately SHM.

A person weighs about 1/6th on the moon compared to Earth due to the moon's weaker gravitational pull. Weight = mass × gravity, and while mass stays constant, the moon's gravity is ~16% of Earth's. The person would feel much lighter, not heavier or the same.

The Moon's gravity is approximately 1/6th (about 16.6%) of Earth's gravity. This is because the Moon has much less mass than Earth - about 1/81th of Earth's mass. On the Moon, objects weigh much less, which is why astronauts could jump much higher and carry heavier equipment easily.

The Moon has about 1/80th of Earth's mass, which is why it has much weaker gravity (about 1/6th of Earth's surface gravity). This significant mass difference explains why the Moon orbits Earth rather than them orbiting a common center of mass. The fraction 1/4 would make the Moon far too massive.

A person would weigh LESS on Mars, not more. Mars has only about 38% of Earth's gravity (mass is 0.107 Earths). A 100 kg person on Earth would weigh about 38 kg on Mars, not 158 kg. The question correctly identifies this as false.

The statement is FALSE. Centre of mass and centre of gravity are not always identical. Centre of mass is a geometric property based on mass distribution, while centre of gravity depends on the gravitational field. They coincide only in uniform gravitational fields.

The Moon's surface gravity is about 1/6th of Earth's gravity. Therefore, a person weighing 60 kg on Earth would weigh only about 10 kg on the Moon. This is why astronauts could jump much higher on the lunar surface. The Moon still has gravity (it's what keeps astronauts from floating away), it's just weaker.

The acceleration due to gravity g in the FPS (Foot-Pound-Second) system is approximately 32.17 ft/s². This is equivalent to 9.81 m/s² in the SI (metric) system. The FPS system uses feet and seconds as base units, so the numerical value differs from the more familiar 9.81.

The acceleration due to gravity in FPS (Foot-Pound-Second) system is 32.17 ft/s². Option A (9.81) is the value in SI/MKS system (m/s²), which is a common point of confusion. The FPS system uses feet as the unit of length, so the value must be larger numerically.

This is a humorous play on the relationship between Earth's rotation and the length of a day. If Earth rotated 30 times faster, each day would be 30 times shorter, so you'd theoretically get paid 30 times more frequently (though your daily wage would remain the same). It's a joke about time perception, not physics.