Problem 694 - JEE Physics

Question

If mass of a body is \(\mathrm{M}\) on the earth surface, than the mass of the same body on the moon surface is (A) \(\mathrm{M} / 6\) (B) 56 (C) \(\mathrm{M}\) (D) None of these

Step-by-Step Solution

Answer

The mass of a body remains constant regardless of its location. Hence, if the mass of a body on Earth is \(\mathrm{M}\), its mass on the Moon's surface would also be \(\mathrm{M}\). So, the correct answer is (C) \(\mathrm{M}\).

Step 1: Recall the Concepts of Mass and Weight

Mass is a scalar quantity that measures the amount of matter present in a body, whereas weight is a vector quantity, indicating the force with which the body is attracted towards the center of the Earth (or any celestial body) due to gravity. The mass of an object remains constant regardless of where it is located, while its weight will change depending on the gravity of the celestial body it's located on.

Step 2: Identify Mass on Earth and Moon

Given the mass of a body on the Earth's surface is represented by M, we need to find the mass of the same body on the Moon's surface. When a body is moved from one celestial object (like Earth) to another (like the Moon), it's important to remember that the body's mass remains unchanged. Although the body's weight may change, its mass, or the amount of matter within it, does not change.

Step 3: Select the Correct Option

Since the mass of an object does not change based on its location, we can conclude that the mass of the body on the Moon's surface would also be M. So, the correct answer is: (C) \(\mathrm{M}\)

Key Concepts

Mass Conservation

Mass conservation is an important principle in physics, stating that the mass of an object does not change regardless of its location or the circumstances around it. When you measure the mass of a backpack on Earth, it remains that same mass whether you take it to another continent or even the Moon. This is because mass is primarily concerned with the amount of matter an object comprises, and that amount doesn't fluctuate between destinations.

• Mass is constant across the universe.
• Measured in kilograms (kg), grams (g), etc.
• Doesn't change with location.

Remember, when you are solving problems involving mass and location, reaffirm that the mass doesn't change. It's a stabilized measure and aids in understanding other related concepts like force and weight.

Gravity on Different Celestial Bodies

Gravity varies across different celestial bodies because it relies on the mass and radius of the particular body in question. That's why you'd weigh less on the Moon compared to Earth. The Moon's gravitational pull is only about 1/6th that of Earth's.

• Earth's gravity: Approximately 9.81 m/s².
• Moon's gravity: Around 1.625 m/s².
• This difference affects weight, not mass.

Every celestial body exerts a specific gravitational force on objects, and this is why weights differ depending on where you are. Remember, weight is the force of gravity acting on your mass: it changes, unlike your mass. This concept is vital if you're tackling astronomy or physics problems that include planetary movement.

Mass and Weight Relationship

Understanding the relationship between mass and weight is crucial. Mass is an intrinsic property, while weight is an extrinsic property dependent on gravity. They are related through the equation: \[\text{Weight (W)} = \text{Mass (M)} \times \text{Gravity (g)}\]Thus, if you travel to a place with different gravity, like the Moon, your weight changes, but not your mass.

• Mass is measured in kilograms (kg).
• Weight is measured in newtons (N).
• Weight equals mass times gravity's acceleration.

Remember that while mass and weight are interconnected, they are distinct concepts used to describe objects in physics. This differentiation is crucial for those venturing into fields involving physical sciences or engineering.