A rod with circular cross-section of radius 5 mm is stretched such that its cross-section remains circular. If after stretching the rod its length becomes four times the original length, then what is the radius of the new cross-section ?

When a rod is stretched, its total volume remains constant. The volume (V) of a rod with a circular cross-section is calculated using the formula for a cylinder: V = πr²L, where r is the radius and L is the length.

Let the initial state be (r₁, L₁) and the final state be (r₂, L₂). According to the law of conservation of volume:

πr₁²L₁ = πr₂²L₂

Given that the new length L₂ = 4L₁ and the initial radius r₁ = 5 mm, we substitute these into the equation:

r₁²L₁ = r₂²(4L₁)
r₁² = 4r₂²
r₂ = r₁ / √4 = r₁ / 2

Substituting r₁ = 5 mm, we get r₂ = 5 / 2 = 2.5 mm. Therefore, the radius of the new cross-section is 2.5 mm.