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. 20 cm/sec
• C. 10 cm/sec
• D. None of these.

Answer 1

Answer: (B)

20 cm/sec

Answer 2

According to the equation of continuity,

Av = av′

⇒ v′ = (A/a)v

where A = πR² and a = πr².

⇒ v′ = v

= $\left( \frac { 1 \mathrm {~cm} } { 0.05 \mathrm {~cm} } \right) ^ { 2 }$ (1 cm/sec)

= 20 cm/sec.

Therefore (2).