Question

F varies jointly as q1 and q2 and inversely as the square d.If F= 80 when q1 =4 q2 =16 and d= 0.4Determine F when q1 =12 q2 =20 and d=0.2

Answer 1

We know that F varies jointly with q1 and q2 and inversely as the square of d, that means that we can write it as:

`F=k(q_1q_2)/(d^2)`

where k is a constant. To find k we plug the values given and solve the equation:

`\begin{gathered} 80=k(4\cdot16)/(0.4^2) \\ 80=k(64)/(0.16) \\ 80=400k \\ k=(80)/(400) \\ k=(1)/(5) \end{gathered}`

Hence the expression for F is:

`F=(q_1q_2)/(5d^2)`

Now, plugging the values given we have:

`\begin{gathered} F=((12)(20))/(5(0.2)^2) \\ F=1200 \end{gathered}`

Therefore F=1200.