Question

velocity of light, gravitational constant, Planck's constant are to be chosen as fundamental units find dimensions of time in the system,mass, and length​

Answer 1

hey
mark as BRAINLIEST ANSWER
follow me
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.