wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The relative densities of concrete and sawdust are 2.4 and 0.3 respectively. For this sphere to float with its entire volume submerged under water, the ratio of the mass of concrete to the mass of sawdust will be


A

8

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

4


Let m be the mass of concrete and ρ its density and let m' be the mass of sawdust and ρ its density.
Then
m=4π3(R3r3)ρ
and m=4π3r3ρ
mm=R3r3r3.ρρ ..... (i)
Since the entire volume V =4π3R3 of the sphere is submerged under water, we have, from the principle of flotation,
Weight of concrete + Weight of sawdust = weight of volume V of water displaced
mg+mg=Vρ0gm+m=Vρ0
where ρ0 is the density of water.
Thus, 4π3(R3r3)ρ+4π3r3ρ=4π3R3ρ0
(R3r3)d+r3d=R3 ..... (ii)
where d=ρρ0 and d=ρρ0 are the relative densities of concrete and sawdust respectively.
Equation (ii), on simplification, gives R3r3=(dd)(d1)
R3r31=(dd)(d1)1
R3r3r3=(1d)(d1) .... (iii)
Using (iii) in (i) and noting that ρρ=dd, we have
mm=(1d)(d1)×dd=(10.3)(2.41)×2.40.3=4
Hence, the correct choice is (b).


flag
Suggest Corrections
thumbs-up
10
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Energy in SHM
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon