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Test Index
JEE Main Physics Class 11 Properties of Solids and Liquids Questions Part 2 Questions
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© examsnet.com
Question : 42
Total: 100
Consider a solid sphere of radius
R
and mass density
ρ
(
r
)
=
ρ
0
(
1
−
r
2
R
2
)
,
0
<
r
≤
R
.
The minimum density of a liquid in which it will float is:
[8 Jan 2020 (I)]
ρ
0
3
ρ
0
5
2
ρ
0
5
2
ρ
0
3
Validate
Solution:
For minimum density of liquid, solid sphere has to float (completely immersed) in the liquid.
m
g
=
F
B
(
also
V
immersed
=
V
total
)
or
∫
ρ
d
V
=
4
3
π
R
3
ρ
l
[
ρ
(
r
)
=
ρ
0
(
1
−
r
2
R
2
)
0
<
r
≤
R
given
]
⇒
R
∫
0
ρ
0
4
π
(
1
−
r
2
R
2
)
.
r
2
d
r
=
4
3
π
R
3
ρ
l
⇒
4
π
ρ
0
[
r
3
3
−
r
5
5
R
2
]
0
R
=
4
3
π
R
3
ρ
l
4
π
ρ
0
R
3
3
×
2
5
=
4
3
π
R
3
ρ
l
∴
ρ
l
=
2
ρ
0
5
© examsnet.com
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