The value of gravitational constant is G= 6.67x10^-11 Nm2/kg2. Suppose we employ a new system of units in which unit of mass is α kg, the unit of length β m and unit of time is γ s. The value of gravitational constant in terms of new units is-
Answers
Answer:
Correct option is
A
Thus, value of G in CGS system of units is 6.67×10
−8
dynecm
2
/g
2
.
Dimensional formula for G is [M
−1
L
3
T
−2
]
Now, n
1
[M
1
−1
L
1
3
T
1
−2
]=n
2
[M
2
−1
L
2
3
T
2
−2
]
n
2
=n
1
[
M
2
M
1
]
−1
[
L
2
L
1
]
3
[
T
2
T
1
]
−2
Here, n
1
=6.67×10
−11
M
1
=1kg, M
2
=1g=10
−3
kg, L
1
=1m, L
2
=1cm=10
−2
m, T
1
=T
2
=1s
Substituting in above equation we get,
n
2
=6.67×10
−11
[
10
−3
kg
1kg
]
−1
[
10
−2
m
1m
]
3
[
1s
1s
]
−2
or, n
2
=6.67×10
−8
Thus, value of G in CGS units is 6.67×10
−8
dynecm
2
/g
2
.
The value of gravitational constant in the new system of units is 6.67 × 10^-11 kg^-1 m^3 s^-2 (α / β^2) (γ^2).
To find the value of the gravitational constant in the new system of units, we need to express the units of mass, length, and time in terms of their SI units, and then substitute these values in the formula for G.
Let the units of mass, length, and time in the new system be M, L, and T, respectively. Then,
Mα kg = M (SI units)
Lβ m = L (SI units)
Tγ s = T (SI units)
Equating the units on both sides, we get:
[M] = kg / α
[L] = m / β
[T] = s / γ
Now, substituting these values in the formula for G, we get:
G = 6.67 × 10^-11 N m^2/kg^2
= 6.67 × 10^-11 [(kg / α) (m / β)^2] / [(s / γ)^2]
= 6.67 × 10^-11 kg^-1 m^3 s^-2 (α / β^2) (γ^2)
Therefore, the value of gravitational constant in the new system of units is 6.67 × 10^-11 kg^-1 m^3 s^-2 (α / β^2) (γ^2).
#SPJ3