Verified Solution • 2025–26 Session moderate

QJEEM19Ph2a5c: JEE Main 2019 Physics - Class 11 JEEM19Ph2a5c Solution: A wooden block floating in a bucket of water has 4/5 of its…

A wooden block floating in a bucket of water has 4/5 of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is :-

Multiple Choice Options

  • A 0.8
  • B 0.7
  • C 0.6
  • D 0.5

Step-by-Step Verified Solution

In 1st situation
Vb ρ\rho bg = Vs ρ\rho wg

VsVb=ρbρw=45{{{V_s}} \over {{V_b}}} = {{{\rho _b}} \over {{\rho _w}}} = {4 \over 5}     ...(i)

Here Vb is volume of block
Vs is submerged volume of block
ρb\rho _b is density of block
ρw\rho _w w is density of water & Let ρo\rho _o is density of oil
Finally in equilibrium condition

Vb ρb\rho _b g = Vb2ρog+Vb2ρwg{{{V_b}} \over 2}{\rho _o}g + {{{V_b}} \over 2}{\rho _w}g

2ρb=ρ0+ρw2{\rho _b} = {\rho _0} + {\rho _w}

⇒ρoρw=35=0.6\Rightarrow {{{\rho _o}} \over {{\rho _w}}} = {3 \over 5} = 0.6

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