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MHT CET 2020 Physics Solved Paper
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© examsnet.com
Question : 1
Total: 50
For the same cross-sectional area and for a given load, the ratio of depressions for the beam of a square cross-section and circular cross-section is
3
:
π
π
:
3
1
:
π
π
:
1
Validate
Solution:
δ
=
W
ℓ
3
3
Y
I
, where
W
=
load,
ℓ
=
length of beam and
I
is geometrical moment of inertia for rectangular beam,
I
=
b
d
3
12
where
b
=
breadth and
d
=
depth
For square beam
b
=
d
∴
I
1
=
b
4
12
For a beam ofcircular cross-section,
I
2
=
(
π
r
4
4
)
∴
δ
1
=
W
ℓ
3
×
12
3
Y
b
4
=
4
W
ℓ
3
Y
b
4
(for sq. cross-section)
and
δ
2
=
W
ℓ
3
3
Y
(
π
r
4
∕
4
)
=
4
W
ℓ
3
3
Y
(
π
r
4
)
(for circular cross-section)
Now
δ
1
δ
2
=
3
π
r
4
b
4
=
3
π
r
4
(
π
r
2
)
2
=
3
π
(
∵
b
2
=
π
r
2
i.e., they have same cross-sectional area)
© examsnet.com
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