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 4 kg weighs 12 N. Calculate the mass of another object that weighs 21 N. kg=

Answer 1

The weight(w) of an object varies directly with the mass(m) of the object.

`w\alpha m`

Introducing a constant k

`w=km`

Given

`\begin{gathered} w=12N \\ m=4kg \end{gathered}`

Substitute the values of the weight and mass in order to solve for k

`\begin{gathered} 12=4k \\ k=(12)/(4)=3 \\ \therefore k=3 \end{gathered}`

Hence, the equation connecting the weight and mass is

`w=3m`

Let us now solve for the mass given the weight to be 21N

`\begin{gathered} 21=3m \\ m=(21)/(3)=7 \\ \therefore m=7kg \end{gathered}`

Hence, the answer is 7kg.