A block of wood is floating in water such that 1/2 of it is submerged in water. When the same block is floated in alcohol, l/3^rd of it's volume is submerged. Now a mixture of water and alcohol is made taking equal volume of both and block is floated in it. What is the % of it's volume that is now submerged?

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$\begin{array}{l} mg = ρ_{1} \times 0 .5 V_{0} g \Rightarrow ρ_{1} = \frac{2 m}{V_{0}} \\ mg = ρ_{2} \times \frac{V_{0}}{3} g \Rightarrow ρ_{2} = \frac{3 m}{V_{0}} \\ ρ = \frac{ρ_{1} V + ρ_{2} V}{2 V} = \frac{ρ_{1} + ρ_{2}}{2} ∣ \\ mg = ρVg = \frac{(ρ_{1} + ρ_{2}) Vg}{2} \end{array} \begin{array}{l} \Rightarrow m = \frac{1}{2} (\frac{2 m}{V_{0}} + \frac{3 m}{V_{0}}) V \\ m = \frac{5 mV}{2 V_{0}} \\ V = 0 .4 V_{0} \Rightarrow 40 % \end{array}$

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET