Apiece of 6 cm long weighs 30 grams. what is the weight of a 8 m length of the same wire

The weight of a 8 m length of the same wire is 4 kg

Since the piece of wire is 6 cm long and weighs 30 grams, we need to find the linear density of the wire, ρ.

The linear density ρ = mass of wire, m/length of wire, L

So, ρ = m/L

Since mass of wire, m = 30 grams and length of wire, L = 6 cm,

ρ = m/L

ρ = 30 g/6 cm

ρ = 5 g/cm

Since we require the weight of 8 m length of wire, the weight of this 8 m length of wire, M = linear density, ρ × length of wire, L'

M = ρL'

Since ρ = 5 g/cm and L' = 8 m = 8 m × 100 cm/1 m = 800 cm (since 1 m = 100 cm)

M = ρL'

M = 5 g/cm × 800 cm

M = 4000 g

M = 4 kg

So, the weight of a 8 m length of the same wire is 4 kg

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