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 (WB) = 240 N
mass of object A (mA) = 3× [mass of object B (mB)]
⇒ mA = 3mB
We have, Weight = mg
Here acceleration due to gravity is constant.
Hence, weight of a body is directly proportional to its mass.
⇒ W ∝ m
⇒ WA/WB = mA/mB
⇒ WA/240 = 3mB/mB
⇒ WA/240 = 3 ⇒ WA = 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 (WE) = 150 N
Acceleration due to gravity on earth (gE) = 9.8 m/s2
Acceleration due to gravity on moon (gM) = 1.625 m/s2
Weight of a body on moon (WM) = ?
We know, Weight (W) = mg
Here mass of the body is constant.
So, W ∝ g
⇒ WE/WM = gE/gM
⇒ 150/WM = 9.8/1.625
⇒ 150/WM = 6 ⇒ WM = 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 (mA) = 60 kg
Weight of body B (WB) = ¼ × [Weight of body A (WA)]
Mass of body B (mB) = ?
We know, Weight (W) = mg
Here the acceleration due to gravity is constant.
Hence, W ∝ m
WA/WB = mA/mB
⇒ WA/(¼WA) = 60/mB
⇒ 4 = 60/mB ⇒ mB = 60/4 = 15 kg
Hence, the mass of body B is 15 kg
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