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 cross-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)impliespir_(1)^(2)xx0.5=pir_(2)^(2)xxv_(2)`
Where `r_(1)-` radius of syringe, `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=50`m