Question

On a given planet, the weight of an object varies directly with the mass of the object. suppose that an object whose mass is 5 kg weighs 20 n . calculate the mass of another object that weighs 32 n .

Answer 1

Since the mass and weight vary directly, they are linked by an expression like

$w = km$

where w is the weight, m is the mass and k is the constant which gives the proportion.

Approach 1:

We may deduce the value of k from the first example: if 5kg weight 20N, then

$20 = 5k \implies k = \frac{20}{5} = 4$

And once k is known, solve the second example for m:

$32 = 4m \implies m = \frac{32}{4} = 8$

Approach 2:

Since the two quantity vary directly, they are in proportion. So, we can write a proportion like

mass1 : weight1 = mass2 : weight2

and solve it for mass2:

$5 : 20 = m : 32 \implies m = \frac{5\cdot 32}{20} = \frac{32}{4} = 8$

Of course, both approaches give the same result.