Weight Formula

It is known that every object is pulled towards the center of the earth by a force of gravity. Hence, the weight of a body is defined as the force of gravity that acts on the mass of a body.  Weight is equal to the product of the mass of a body and acceleration due to gravity. Weight is depicted as W and the SI unit of weight is Newton (N). It is a vector quantity that is directed towards the center of the earth.

Weight Formula

Weight of the body (W) = mass of the body (m) × acceleration due to gravity (g)

i.e., W = mg

From the formula of weight, we can say that weight depends on the mass of a body and the acceleration due to gravity. The mass of a body doesn’t change, but the acceleration due to gravity changes with respect to the location of the body. Hence, the weight of a body changes with respect to the location of the object. For example, the weight of a body on the moon is 1/6 times the weight of the body on the earth, since acceleration due to gravity on the moon is 1/6 times of acceleration due to gravity on earth.

Solved Problems

Problem 1: Calculate the weight of a body on earth if its mass is 45 kg?

Solution:

Given data, Mass of the body = 45 kg.

We know that g = 9.8 m/s²

We have, Weight (W) = mg

⇒ W = 45 × 9.8 

⇒ W = 441 N

Hence, weight of the body (W) = 441 N

Problem 2: Find the mass of a body, if its weight on the moon is 100 N. The acceleration due to gravity on the moon is 1.625 m/s².

Solution: 

Given data, Weight of the body on moon = 100 N

Acceleration due to gravity on moon = 1.625 m/s²

We have, Weight (W) = mg

⇒ 100 = m × 1.625

⇒ m = 100/1.625 ⇒ m = 61.54 kg

Hence, mass of the body (m) = 61.54 kg

Problem 3: Prove that acceleration due to gravity on earth is 9.8 m/s² if the mass of a body and weight is 30 kg and 294 N respectively.

Solution:

Given data, Weight of body = 294 N

Mass of the body = 30 kg

We have, Weight (W) = mg

⇒ 294 = 30 g

⇒ g = 294/30

⇒ g = 9.8 m/s²

Hence it is proved that acceleration due to gravity on earth is 9.8 m/s².

Problem 4: The weight of a box on earth is 490 N. Calculate the mass of the box in grams. (g = 9.8 m/s²)

Solution:

Given data, Weight of a box on earth (W) = 490 N

Acceleration due to gravity (g) = 9.8 m/s²

Mass of the box (m) = ?

We have, Weight (W) = mg

⇒ 490 = m × 9.8

⇒ m = 490/9.8 = 50 kg

We know that 1kg = 1000 grams

Hence, mass of the box = 50 kg = 50 × 1000 grams = 50,000 grams

Problem 5: Find the weight of object A, if the mass of object A is thrice the mass of object B and the weight of object B is 240 N?

Solution:

Given data, Weight of object B (W_B) = 240 N

mass of object A (m_A) = 3× [mass of object B (m_B)]

⇒ m_A = 3m_B

We have, Weight = mg

Here acceleration due to gravity is constant.

Hence, weight of a body is directly proportional to its mass.

⇒ W ∝ m

⇒  W_A/W_B = m_A/m_B

⇒ W_A/240 = 3m_B/m_B

⇒ W_A/240 = 3 ⇒ W_A = 3 × 240 = 720 N

Hence, weight of the object B is 720 N

Problem 6: Find the weight of a body on the moon, if its weight on earth is 150N? Acceleration due to gravity on earth = 9.8 m/s² and acceleration due to gravity on moon = 1.625 m/s².

Solution:

Given data, Weight of a body on earth (W_E) = 150 N

Acceleration due to gravity on earth (g_E) = 9.8 m/s²

Acceleration due to gravity on moon (g_M) = 1.625 m/s²

Weight of a body on moon (W_M) = ?

We know, Weight (W) = mg

Here mass of the body is constant.

So, W ∝ g

⇒  W_E/W_M = g_E/g_M

⇒ 150/W_M = 9.8/1.625

⇒  150/W_M = 6 ⇒  W_M = 150/6 = 25 N

Hence, weight of the body on moon is 25N

Problem 7: Find the mass of body B, if its weight is one-fourth of the weight of object A. Mass of the body A = 60 kg.

Solution:

Given data, Mass of body A (m_A) = 60 kg

Weight of body B (W_B) = ¼ × [Weight of body A (W_A)]

Mass of body B (m_B) = ?

We know, Weight (W) = mg

Here the acceleration due to gravity is constant.

Hence, W ∝ m

W_A/W_B = m_A/m_B

⇒ W_A/(¼W_A) = 60/m_B

⇒ 4 = 60/m_B ⇒  m_B = 60/4 = 15 kg

Hence, the mass of body B is 15 kg