Question

the weight of a piece of wire is directly proportional to its length. A piece of wire is 25cm long and has a weight of 6 grams. Another piece of the same wire is 30cm long.Calculate the weight of the 30cm piece of wire p is inversely proportional to m.p=48 when m=9 Calculate the value of p when m =12.

Answer 1

Part A

Weight of a piece of wire is directly proportional to its length

⇒ Weight of wire piece (W) α Length of wire (L)

⇒ W = k × L

When L = 25 cm, then W = 6 gms

⇒ $\frac{W}{L}$ = k

⇒ k = $\frac{6}{25}$

To calculate weight of 30 cm wire, put value of k and W in the expression W = k × L

⇒ W = $\frac{6}{25}$ × 30

⇒ W = 7.2 gms

Part B

p α m

⇒ p = k × m

If p=48 and m=9

k = $\frac{p}{m}$

⇒ k =  $\frac{48}{9}$

Now to calculate p when m = 12, substitute the value of m and k in p = k × m

p = $\frac{48}{9}$ × 12

⇒ p = 64