Question

One newton equals about 100 g on Earth. How many newtons would a football weigh if it had a mass of 400 g?

Answer 1

Hint: Newton is the unit of force which is named after Sir Isaac Newton as a recognition of the work on classical mechanics. One newton is defined as the force that is required to accelerate the mass of one kg one meter per second squared.

Complete step by step solution:
Given data:
Mass of the object = 100 g = 0.1 kg
Mass of the football = 400 g = 0.4 kg
Weight of the football =?
First, consider for 100 g object:
We know that weight = mg
$\Rightarrow g={\displaystyle \frac{weight}{m}}$
$\Rightarrow g={\displaystyle \frac{1N}{0.1kg}}$
$\Rightarrow g=10m/s^2$
Considering for football of mass 400 g:
Again by using the formula, weight = mg, we get
$weight=0.4\times 10=4N$ $\left(\because g=10m/s^2\right)$
Hence the weight of football is 4 N.

Additional Information:
1. The mass will never be zero. It is a scalar and has the only magnitude. The mass can be measured by using an ordinary balance.
2. The weight can be zero. It is a vector quantity and thus will have both magnitude and direction. Weight varies according to the locations. Weight can be measured by using a spring balance.

Note: 1. The mass is a fundamental quantity and is defined as the measure of the amount of matter in a body. The units of mass are gram, kilogram, and tonne. Mass is a quantitative measure of inertia. Mass always remains the same.
2. The weight is defined as the measure of the force of gravity acting on the object. In weight, changes occur only when the acceleration due to gravity changes. The unit of weight is Newton.