Gravitation and Center of Mass

The formula for acceleration due to gravity at depth 'd' from Earth's surface is gd = g(1 - d/R), where g is surface gravity and R is Earth's radius. This shows that gravity decreases linearly as we go deeper inside Earth, becoming zero at the center.

Mass is an intrinsic property of matter and does not change with location. A 42 kg mass on Earth remains 42 kg on the Moon - only the weight (force of gravity acting on that mass) changes. Weight would be about 1/6th on the Moon (approximately 7 kg force), but mass stays constant at 42 kg.

Gravitational force is directly proportional to mass (F = G×m1×m2/r²). A body with greater mass experiences a stronger gravitational pull. This is why more massive objects weigh more on Earth. The relationship is linear - doubling the mass doubles the gravitational force acting on it.

Earth's mass is approximately 5.972 × 10^24 kg. Option C (5.976 × 10^24 kg) is the closest approximation among the choices and is the accepted value in many textbooks. Options A, B, and D are incorrect values.

True. Scientists estimate the total mass of Earth's atmosphere at approximately 5.5 quadrillion (5.5 × 10^15) tons. This is based on atmospheric pressure at sea level and Earth's surface area.

The actual amount of cosmic dust and meteoritic material entering Earth's atmosphere is estimated at around 40,000 tons per year, far exceeding the claimed 1,000 tons. This makes the statement false.

The moon's gravitational force is approximately 1/6 of Earth's. If Earth's gravity is standardized to 1, the moon's gravity would be about 0.167. This is why astronauts could jump much higher on the lunar surface during Apollo missions - their effective weight was only 16.7% of Earth's.

Mars has approximately 38% of Earth's gravitational force (about 3.7 m/s² vs Earth's 9.8 m/s²). If Earth's gravity is 1, Mars' gravity is 0.38. This means a 100 kg person would feel like they weigh only 38 kg on Mars, which is still significantly more than on the moon.

The sun's surface gravity is approximately 27.9 times Earth's (274 m/s² vs 9.8 m/s²). If Earth's gravity is 1, the sun's gravity is about 27.9. This intense gravity results from the sun's enormous mass - about 330,000 times Earth's mass - compressed into a sphere, making the sun roughly 109 times Earth's diameter.

Mercury's gravitational force is approximately 0.38 times Earth's (about 3.7 m/s²), or 37-38% of Earth's gravity. This is very similar to Mars' gravity, as both planets are smaller and less massive than Earth. Despite being the smallest planet, Mercury's high density gives it gravity comparable to Mars.

Jupiter has a surface gravity about 2.5 times that of Earth (24.79 m/s² vs 9.81 m/s² = 2.53g). Despite being a gas giant with no solid surface, its immense mass creates extremely strong gravitational pull at its cloud tops.

Neptune has a surface gravity of about 1.14g relative to Earth (11.15 m/s² vs 9.81 m/s²). Neptune is more dense than Uranus despite being similar in size, giving it stronger surface gravity than Earth.