A tank is filled up to a height 2 H with a liquid and is placed on a platform of height H from the ground. The distance x from the ground where a small hole is punched to get the maximum range R is

Question

A tank is filled up to a height 2 H with a liquid and is placed on a platform of height H from the ground. The distance x from the ground where a small hole is punched to get the maximum range R is (A) H (B) 1.25 H (C) 1.5 H (D) 2 H

Tardigrade Admin · Accepted Answer

As x=(1/2) g t2 ⇒ t=√(2 x/r) Velocity of efflux v=√2 g(H-x) Hence R=v t=2 √x(3 H-x) For range to be maximum (d R/d x)=0 which gives x=(3/2) H=1.5 H Alternatively: Maximum range is also equal to average of two heights x=(H+2 H/2)=(3 H/2)=1.5 H

Q. A tank is filled up to a height $2 H$ with a liquid and is placed on a platform of height $H$ from the ground. The distance $x$ from the ground where a small hole is punched to get the maximum range $R$ is

$H$

$1.25 H$

$1.5 H$

$2 H$

Q. A tank is filled up to a height 2H with a liquid and is placed on a platform of height H from the ground. The distance x from the ground where a small hole is punched to get the maximum range R is

H

1.25H

1.5H

2H

As x=21​gt2⇒t=r2x​​ Velocity of efflux v=2g(H−x)​ Hence R=vt=2x(3H−x)​ For range to be maximum dxdR​=0 which gives x=23​H=1.5H Alternatively: Maximum range is also equal to average of two heights x=2H+2H​=23H​=1.5H

Q. A tank is filled up to a height $2 H$ with a liquid and is placed on a platform of height $H$ from the ground. The distance $x$ from the ground where a small hole is punched to get the maximum range $R$ is

$H$

$1.25 H$

$1.5 H$

$2 H$