A water tank has cross-sectional area 750 cm². Water leaves through a tap of area 500 mm² with speed 30 cm s⁻¹. At that instant, dh/dt = −x × 10⁻³ m s⁻¹. Find x.
Physics · Circular Motion
JEE Mains JEE Advanced

Question

A water tank has cross-sectional area 750 cm². Water leaves through a tap of area 500 mm² with speed 30 cm s⁻¹. At that instant, dh/dt = −x × 10⁻³ m s⁻¹. Find x.

G1 Physics · Accepted Answer

Using continuity: A₁v₁ = A₂v₂ A₁ = 750 cm² = 750 × 10⁻⁴ m² A₂ = 500 mm² = 500 × 10⁻⁶ m² v₂ = 30 cm s⁻¹ = 0.30 m s⁻¹ v₁ = A₂v₂/A₁ = (500 × 10⁻⁶ × 0.30)/(750 × 10⁻⁴) = 2 × 10⁻³ m s⁻¹ Since the water level falls: dh/dt = −2 × 10⁻³ m s⁻¹ Hence x = 2.