Question
Answer (177)
Answer:
Young's modulus is the ratio of stress, whose unit is pressure to strain (which has no unit as it is length divided by length) and hence its dimensiional formula is given by pressure units i.e.
Force
Area
As we have
M
×
L
T
2
for force and
L
2
for area,
dimensional formula for Young's mdulus is
M
L
T
2
L
2
=
M
1
L
−
1
T
−
2
But if we chose
F
for force (whose dimension is
M
L
T
−
2
),
A
for acceleration (whose dimension is
L
T
−
2
) and
V
for velocity (whose dimension is
L
T
−
1
.
we can get Young's modulus as pressure i.e. Force divided by Area. Here we have Force as
F
and regarding area we can work out using acceleration and velocity as
a
=
V
4
A
2
=
(
L
T
−
1
)
4
(
L
T
−
2
)
2
=
L
2
, note here
A
represents acceleration not area.
Hence in terms of
F
,
A
and
V
, Young's modulus is
F
V
4
A
2
=
F
V
−
4
A
2