Gravitation

Concept: It is crucial to distinguish between mass and weight.
Mass is a measure of the amount of matter in an object. It is an intrinsic property of the object and remains constant regardless of its location. The SI unit of mass is the kilogram (Kg).
Weight is the force of gravity acting on an object. It depends on both the mass of the object and the acceleration due to gravity at its location ( ). The SI unit of weight is the Newton (N). Step 1: Identify the given quantity The mass of the man on Earth is given as . Step 2: Understand how mass changes with location Mass is an inherent property of an object, representing the quantity of matter it contains. This quantity of matter does not change whether the man is on Earth, on the Moon, or anywhere else in the universe (unless he gains or loses actual matter, which is not the case here). Step 3: Consider the effect of the Moon's gravity The Moon has a weaker gravitational pull than Earth. The acceleration due to gravity on the Moon is approximately of that on Earth ( ). This means the man's {weight} on the Moon would be different (approximately of his weight on Earth). If his weight on Earth is , his weight on the Moon would be . If we were considering "effective mass" based on weight, then 10Kg might seem plausible, but the question explicitly asks for "mass". Step 4: Determine the man's mass on the Moon Since mass is a constant property and does not depend on the gravitational field, the man's mass on the Moon will be the same as his mass on Earth. Therefore, his mass on the Moon will still be . Option (2) would be related to his weight on the moon if was roughly , then his weight on Earth would be . His weight on the moon would be . If this weight was divided by Earth's ( ), you'd get an "equivalent Earth mass" of , but this is a misinterpretation of the question. The question asks for mass, not an equivalent mass based on lunar weight compared to Earth's gravity. Option (3) might come from confusing mass with weight in Newtons (e.g., if , a mass has a weight of ), but mass is in Kg. The correct answer is that his mass remains .

Step 1: Analyze the event described.
A boy hits a mango tree with a stone, and a mango falls down. We need to identify the fundamental force or principle responsible for the mango's downward motion. Step 2: Evaluate the given options.

(1) Due to gravitational force of earth: The Earth exerts a gravitational force on all objects with mass, pulling them towards its center. This force is commonly referred to as gravity. When an object is no longer supported (like a mango detached from a tree), gravity is the force that causes it to fall downwards.
(2) Due to friction: Friction is a force that opposes motion between surfaces in contact. While air resistance (a type of friction) might affect the mango's fall by slowing it down, it is not the cause of the fall itself.
(3) Due to acceleration: Acceleration is the rate of change of velocity. The mango \textit{accelerates} downwards due to gravity, but acceleration is an effect of the force, not the cause of the fall itself. The cause of the acceleration is the gravitational force.
(4) None of these: This option would be correct only if none of the other options explained the phenomenon. Step 3: Conclude the primary reason for the mango falling.
The primary reason the mango falls down once it's dislodged from the tree is the Earth's gravitational pull. Step 4: Compare with the given options.
The phenomenon is explained by the gravitational force of the Earth. (1) Due to gravitational force of earth

Step 1: Recall Newton's Universal Law of Gravitation.
Newton's Universal Law of Gravitation states that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Step 2: Express the law mathematically.
The mathematical formula for this law is typically written as: or where:
is the gravitational force between the two objects.
is the gravitational constant.
and are the masses of the two objects.
or is the distance between the centers of the two objects. Step 3: Analyze the given options.
Option (1) is . This formula uses and to represent the two masses, which is a common notation. So, this is a valid representation of the Universal Law of Gravitation.
Option (2) is . This formula uses and to represent the two masses, which is also a common notation. So, this is a valid representation of the Universal Law of Gravitation.
Option (3) is . This formula represents the weight of an object (the force of gravity on an object near a planet's surface), where is the acceleration due to gravity. This is a specific case derived from the Universal Law of Gravitation, but it is not the Universal Law itself. Step 4: Conclude which options are correct.
Both options (1) and (2) correctly represent the Universal Law of Gravitation, just using different variable names for the masses. Therefore, the correct answer is that both 1 and 2 are true. $ $