Question

If the ratio of radii of two wires of same material is 3 : 1 and ratio of their lengths is 5 : 1, then the ratio of the normal forces that will produce the same extension in the length of two wires is:

Options

• 2 : 1

• 4 : 1

• 1 : 4

• 1 : 1

Answer 1

1 : 1

Explanation:

Y = `("F"ℓ)/("A"Δℓ)`;

F = `("YA"Δℓ)/ℓ`

`"F"_1/"F"_2 = "A"_1/"A"_2 xx 1_2/1_1`

= `"r"_1^2/"r"_2^2 xx 1_2/1_1`

= `4/1 xx 1/4`

= 1 : 1