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JEE Main 201910 AprilEvening Shift
Exam
JEE Main
Year
2019
Date
10 April
Shift
Evening Shift
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Main 2019 · 10 April · Evening Shift · Physics · Mechanical Properties of Fluids

A cubical block of side 0.5m floats on water with 30% of its volume...

A cubical block of side 0.5m0.5m floats on water with 3030% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water?

[Take, density of water =103kg/m3= {10}^{3}kg / {m}^{3} ]

Options

  1. A87.5kg87.5kg
  2. B65.4kg65.4kg
  3. C30.1kg30.1kg
  4. D46.3kg46.3kg

Correct answer

A. 87.5kg87.5kg

Step-by-step solution

In first case, when 3030% of the cube inside water,
ρwVing=ρcVg{ρ}_{w}{V}_{in}g = {ρ}_{c}Vg
VinV=ρcρw=0.3\dfrac{{V}_{in}}{V} = \dfrac{{ρ}_{c}}{{ρ}_{w}} = 0.3
Additional weight we can put ww is,
Vρwg=ρcVg+wV{ρ}_{w}g = {ρ}_{c}Vg + w
w=Vw = V\left({ρ}_{w} - {ρ}_{c}\right)g<br/><br/>= {\left(0.5\right)}^{3} \times 0.7 \times {10}^{3} \times g<br/><br/>= 87.5gN<br/>Additionofmassthatwecanput<br/>Addition of mass that we can put= 87.5kg
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