Question

M is directly proportional to r²

When r = 5, M = 200

Work out the value of r when M = 288.

Answer 1

`\:\:\:\:\:\:\;\star\small \underline{ \boxed{ \sf{ \pmb{ m∝ r^2 }}}}\\`

`\:\:\:\:\:\:\longrightarrow \sf {m = Kr^2}\\`

On substituting r=5 and m=200

`\:\:\:\:\:\:\longrightarrow \sf {200=K * \bigg(5\bigg)^2}\\`

`\:\:\:\:\:\:\longrightarrow \sf {200 = K* 25}\\`

`\:\:\:\:\:\:\longrightarrow \sf {K = (200)/(25)}\\`

`\:\:\:\:\:\:\longrightarrow \sf {K = \cancel{(200)/(25)}}\\`

`\:\:\:\:\:\:\longrightarrow \sf {\underline{\underline{\pink{k =8}}}}\\`

Now, we are asked to find out the value of r when m is equal to 288.

`\:\:\:\:\:\:\longrightarrow \sf {m = Kr^2}\\`

`\sf \underline{On \:substituting \: k \: = 8\: }\\`

`\:\:\:\:\:\:\longrightarrow \sf {288 = 8* r^2}\\`

`\:\:\:\:\:\:\longrightarrow \sf {r^2 = \cancel{(288)/(8)}}\\`

`\:\:\:\:\:\:\longrightarrow \sf {r^2 =36}\\`

`\:\:\:\:\:\:\longrightarrow \sf {r = √(36)}\\`

`\:\:\:\:\:\:\longrightarrow \boxed{ \tt{ \pmb{ \pink{r = 6 }}}}\\`

`\\ \therefore \underline{ \cal{ \pmb{ \:Value \: of \: r\: is \: \frak{\pink{ 6 \: }.\: When \: m \:= 288 }}}}\\`