JEE Main 2026 Apr 6 Shift 2, Physics Q9: Hydrodynamic

JEE Main2026Apr 6, Shift 2Physics

A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is 528 dm $^{3}$ (dm: decimeter). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 70 cm below the top of water level, then horizontal range of water falling on the ground in the beginning is ____ cm.

A
$1202$
B
$1402$
C
$1403$
D
$1203$

Solution

Step 1. Find vessel height from capacity. $V = π r^{2} h$ with $r = 0.4$ m and $V = 528 \times 1 0^{- 3}$ m $^{3}$ :

$h = \frac{528 \times 1 0 ^{- 3} \times 7}{( 0.4 ) ^{2} \times 22} = 1.05$ m $= 105$ cm.

Step 2. Efflux speed by Torricelli (head $= 70$ cm above hole):

$u = 2 g (0.70) = 14$ m/s.

Step 3. Hole is $105 - 70 = 35$ cm above vessel base; vessel sits on a block of height $105$ cm, so hole is $35 + 105 = 140$ cm above the ground. Time of fall:

$t = \frac{2 H}{g} = \frac{2 \times 1.40}{10} = 0.28$ s.

Step 4. Range $R = u t = 14 0.28 = 3.92 = 1.96 \times 2 = 1.4 2$ m $= 1402$ cm.

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JEE Main 2026 Apr 6 Shift 2, Physics Q9: Hydrodynamic

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