Question

If Lis inversly proportional to root of m and L=6 when m=4 what is the value of m when L=4​

Answer 1

Let
L = k / √m ________(1)

here k is proportional constant.

since , L = 6 when m = 4 then from (1)

6 = k /√4

6 = k /2

k = 12

put value of ' k ' in eq.(1) , now the equation is :-

L = 12 / √m _______eq(2)

put value of L = 4 here in equation (2),we get

4 = 12 / √m

√m = 12 /4

√m = 3

m = (3)^2

m = 9
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Your Answer : m = 9
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Answer 2

Step-by-step explanation:

Given: L is inversly proportional to root of m.

Therefore

$L \propto \: \frac{1}{\sqrt m} \\ \implies \: L = \frac{k}{\sqrt m} \: \\ where \: k \: is \: an \: arbitrary \: \\ constant. \\ \implies \: L{\sqrt m} \: = k \\ now \: when \: L=6 \: and \: m=4 \\k = ? \\ k \: = 6 \times {\sqrt 4}= 6 \times 2 \\ k = 12 \\ next \: when \: L = \: 4 \: we \: need \: to \\ \: find \: m \\ \because \: k \: = L{\sqrt m} \\ \implies \: 12 = 4{\sqrt m} \\ {\sqrt m} \: = \frac{12}{4} \\ {\sqrt m} = 3\\ m = 9.....(squiring \: both \: sides)$