the pressure of the gas is given by the expression p=aL^2+bL where L is the length. determine the dimensions of b
Answers
Answer:
Explanation:
Given relation
p
=
a
−
t
2
b
x
p has dimension of pressure.
So in rhs both the terms
(
a
and
t
2
b
x
)
added should have same dimensions of pressure.
Now dimension of pressure is
[
M
]
[
L
−
1
]
[
T
−
2
]
x is the distance so it has dimension of length
[
L
]
So dimension of
t
2
b
x
=
[
M
]
[
L
−
1
]
[
T
−
2
]
=
[
T
2
]
[
L
−
1
]
dimension of b
So
dimension of b
=
[
T
4
]
[
M
−
1
]
So the ratio of dimension of
a
and
b
is
=
[
M
]
[
L
−
1
]
[
T
−
2
]
[
T
4
]
[
M
−
1
]
=
[
M
2
]
[
L
−
1
]
[
T
−
6
]
Answer link
A08
Jul 31, 2017
In the given relation
p
=
a
−
t
2
b
x
p
is pressure
∴
on the RHS both the terms also represent pressure.
⇒
dimensions of
t
2
b
x
=
pressure
⇒
b
=
t
2
x
pressure
Since
t
→
T
and
x
→
L
⇒
b
=
T
2
L
pressure
Dimensions of
a
b
=
pressure
T
2
L
pressure
⇒
a
b
=
L
pressure
2
T
2
Since dimensions of pressure are
M
L
−
1
T
−
2
We get
Dimensions of
a
b
=
L
(
M
L
−
1
T
−
2
)
2
T
2
⇒
a
b
=
M
2
L
−
1
T
−
6