Question

A cylindrical vessel of $90cm$ height is kept filled up to the brim. It has four holes four holes $1$, $2$, $3$ and $4$ which are respectively, at height of $20cm$, $30cm$, $40cm$ and $50cm$ from the horizontal floor $PQ$. The water falling at the horizontal distance from the vessel comes from

• A. hole number $4$
• B. hole number $2$
• C. hole number $3$
• D. hole number $1$

Answer 1

Answer: (A), (B), (C)

The correct options are
A hole number $4$
B hole number $2$
C hole number $3$

Horizontal range $R=2\sqrt{h(H-h)}$, where

h is the depth of the hole below free surface of loquid,

H is the total height of liquid

$H=90㎝,h_1=90-20=70cm$

$h_2=90-30=60cm$

$h_3=90-40=50cm$

$h_4=90-50=40cm$

$R_1=2\sqrt{70(90-70)}=2\sqrt{70\times 20}=74.83$

$R_2=2\sqrt{60\times 30}=84.85$

$R_3=2\sqrt{50\times 40}=89$

$R_4=2\sqrt{40\times 10}=89$

Hence, range is maximum for hole $2,3$ & $4$