Q.

A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3 for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust willbe

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away
An Intiative by Sri Chaitanya

a

8

b

4

c

3

d

zero

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

Let specific gravities of concrete and saw dust are ρ1 and ρ2 respectively.According to principle of floatation weight of whole sphere = upthrust on the sphere43π(R3-r3)ρ1g+43πr3ρ2g = 43πR3×1×g⇒R3ρ1-r3ρ1+r3ρ2 = R3⇒R3(ρ1-1) = r3(ρ1-ρ2)⇒R3r3 = ρ1-ρ2ρ1-1⇒R3-r3r3 = ρ1-ρ2-ρ1+1ρ1-1⇒(R3-r3)ρ1r3ρ2 = (1-ρ2ρ1-1)ρ1ρ2⇒Mass of concreteMass of saw dust = (1-0.32.4-1) ×2.40.3 = 4
Watch 3-min video & get full concept clarity
score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

whats app icon
A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3 for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust willbe