Sample Problems on Mass and Weight

Problem 1: The Mass of an object is 10 kg. What is its weight on the earth?

Solution:

Given that, 

Mass (m) = 10 kg

Acceleration due to gravity (g) = 9.8 m s^–2

Expression of the weight is 

W = m × g

Substitute the values in the above equation.

W = 10 kg × 9.8 m s^-2 = 98 N

Thus, the weight of the object is 98 N.

Problem 2: An object weighs 10 N when measured on the surface of the earth. What would be its weight when measured on the surface of the moon?

Solution:

Given,

Weight of an object on Earth is 10 N

Relation between the weight of an object on Earth (W_e)  and weight of an object on Moon (W_m)

W_m = (1⁄6)×W_e

Substitute the value in the above expression.

 W_m = (1⁄6)×10 N

 W_m = 1.67 N

Thus, the weight of the object on the surface of the moon would be 1.67 N.

Problem 3: What is the relation between the weight of an object on the Earth and the weight of an object on the moon?

Solution:

Given,

• Mass of the Earth is 5.98 ×10²⁴ kg.
• Mass of the Moon is 7.36×10²² kg.
• Radius of the Earth is 6.37×10⁶ m.
• Radius of the Moon is 1.74×10⁶ m.

Let the mass of an object be m, the weight on the moon be W_m, the mass of the moon be M_m and its radius be R_m.

From the universal law of gravitation,

W_m = (G M_m m)/(R)²

Substitute the values in the above expression.

W_m = (G 7.36×1022 kg m)/(1.74×10⁶ m)² . . .(1)        

Let the weight of the same object on the earth be W_e, the mass of Earth is M and its radius is R then the expression for the weight of the object on Earth is

W_e = (G M m)/(R)²

Substitute the values in the above expression

W_e = (5.98 ×1024 kg m)/(6.37×10⁶ m)². . .(2)

Divide equation (1) and (2),

W_m/W_e = 2.431 1010/1.474 1011

⇒ W_m/W_e = 0.165

⇒ W_m/W_e ≈ 1/6

⇒ W_m ≈ (1⁄6)×W_e

Mass and Weight are commonly used in the same manner by the general masses but there are differences between both Mass and Weight, where Mass is the measure of Inertia unlike Weight which is a measure of force acting on a body towards the heavy body. But yet still many people use these two terms interchangeably.

As we know that to change the speed or direction of an object, a force is required. If you drop anything from a great height, it will fall towards the earth’s surface. The planet revolves around the Sun and the moon revolves around the earth. There must be some force operating on objects, planets, and other celestial bodies. Isaac Newton noted that the same force is responsible for all these. This force is called gravitational force.