A syringe of diameter 1 cm having a nozzle of diameter 1 mm is placed horizontally at a height 5 m from the ground an incompressible non-viscous liquid is filled in the syringe and the liquid is compressed by moving the piston at a speed of `0.5ms^(-1)` the horizontal distance travelled by the liquid jet is `(g=10ms^(-2))`

Explanation

Let `A_(1)` is corss - sectional area of piston of syringe and `A_(2)` the cross - sectional area of nozzle.
From principle of continuity for non - viscous liquid. `A_(1)v_(1)=A_(2)v_(2)rArr pir_(1)^(2)xx0.5=pir_(2)^(2)xxv_(2)`
Where `r_(1)-"radius of syring, "r_(2)-"radius of nozzle"`
`10^(-4)xx((1)/(2))^(2)xx0.5=10^(-6)xx((1)/(2))^(2)v_(2),v_(2)=50ms^(-1)`
From Torricelli.s theorem,
`h=(1)/(2) g t^(2), 5=(1)/(2)xx10xxt^(2), t = 1s`
This is the time taken for the water jet to reach upto the ground. Horizontal distance
`R=v_(2)xxt=50xx1=50m`