in a new system two units of be introduced if unit of length is 2 metre and 2 second is considered as a unit of time then the unit of speed equal to option a. 2m/s b. 4m/s c. 1m/s d. 0m/s
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2
Answer:
[
m
]
=
c
1
2
G
−
1
2
h
1
2
Explanation:
Here,
[
c
]
=
L
T
−
1
[
G
]
=
M
−
1
L
3
T
−
2
[
h
]
=
M
1
L
2
T
−
1
Let
m
α
c
x
G
y
h
z
By substituting the dimensions of each quantity in both the sides,
M
=
(
L
T
−
1
)
x
(
M
−
1
L
3
T
−
2
)
y
(
M
L
2
T
−
1
)
z
M
=
[
M
y
+
z
L
x
+
3
y
+
2
z
T
x
−
2
y
−
z
]
By equating the power of M, L, T in both the sides:
−
y
+
z
=
1
,
x
+
3
y
+
2
z
=
0
,
−
x
−
2
y
−
z
=
0
By soling the above equation ,
We get,
x
=
1
2
,
y
=
−
1
2
,
and
z
=
1
2
So,
[
m
]
=
c
1
2
G
−
1
2
h
1
2
In above Manner, solve for Length And Time.
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