A container of large uniform cross sectional area A resting on a horizontal surface holds two immiscible non viscous and incompressible liquids of density d and 3d, each of height H/2. The lower density liquid is open to the atmosphere having pressure P0. A tiny hole of area a(a<<A) is punched to the vertical side of lower container at a height h (0<h<H/2) for which range is maximum.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

h = H /3

Range $R = \frac{2 H}{3}$

Range $R = \frac{3 H}{2}$

Velocity of efflux $v = \sqrt{\frac{2}{3} gH}$

answer is A, B, D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Bernoulli’s theorem for an orifice at depth ‘x’ in liquid ‘3d’.
$P_{0} + (dg \frac{H}{2} + 3 dg \cdot x) = P_{0} + \frac{1}{2} \times 3 d \times v^{z}$ ………..(1)
$\frac{H}{2} - x = \frac{1}{2} {gt}^{2}$ ……………………..(2)
R = Vt…………..(3)
Solve for R and apply $\frac{d R}{d x} = 0 f o r$ maxima