A tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is 2 m / s, then velocity of water leaving the point (2) will be

Solution

Physics sir · 3 steps

Area goes as radius squared, so halving the radius makes the water run four times faster.

1. Same flow rate. Water is incompressible, so the volume entering at (1) each second must leave at (2). That means A v is the same at both ends.

   A₁ v₁ = A₂ v₂ ⇒ π r₁² v₁ = π r₂² v₂

2. Put in numbers. v₂ = v₁ (r₁/r₂)² = 2 × (2/1)² = 2 × 4 m/s. The units of radius cancel in the ratio, so there is no need to convert cm to m.
3. So. v₂ = 8 m/s, which is option (d).

The idea to keep. In continuity problems speed scales inversely with area, and area scales with radius squared. Always square the radius ratio before you multiply.

Answer from the NTA final answer key. Solution by PrepWiser.