Question 356: Properties of Matter

Question

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

Accepted Answer

$$F = {{YA} \over L} 	imes \ell $$
So, extension, $$\ell  \propto {L \over A} \propto {L \over {{D^2}}}$$
[$$ 	herefore $$ F and Y are constant]
$${\ell _1} \propto {{100} \over {{1^2}}} \propto 100$$ and $${\ell _2} \propto {{200} \over {{2^2}}} \propto 50$$
$${\ell _3} \propto {{300} \over {{3^2}}} \propto {{100} \over 3}$$ and $${\ell _4} \propto {{50} \over {{1 \over 4}}} \propto 200$$
The ratio of $${L \over {{D^2}}}$$ is maximum for case (length = 50 cm, diameter = 0.5 mm)

Answer

length = 200 cm, diameter = 2 mm

Answer

length = 300 cm, diameter = 3 mm

Answer

length = 50 cm, diameter = 0.5 mm

Answer

length = 100 cm, diameter = 1 mm

Properties of Matter

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

Choose the correct answer: