Question

A piston of a syringe pushes a liquid with a speed of 1 cm/sec. The radii of the syringe tube and the needle are R = 1cm and r = 0.5 mm respectively. The velocity of the liquid coming out of the needle is

• A. 2 cm/sec
• B. 400 cm/sec
• C. 10 cm/sec
• D. None of these

Answer 1

The correct option is B

400 cm/sec

According to the equation of continuity,

Av = av'

$\Rightarrow$ v' = ( $\frac{A}{a}$)v

where A = $\pi R^2$ and a = $\pi r^2$.

$\Rightarrow$ $v^{\prime }={\left(\frac{R}{r}\right)}^2$ $v={\left(\frac{1cm}{0.05cm}\right)}^2$ ( 1cm/sec) = 400 cm/sec.