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A physical energy of the dimension of le...

A physical energy of the dimension of length that can be formula cut of `c,G` and `(e^(2))/(4 pi epsilon_(0))` is [`c` is velocity of light `G` is universal constant of gravilation e is change

A

`(1)/(c^(2)) [G(e^(2))/(4pi epsilon_(0))]^(1//2)`

B

`c^(2) [G(e^(2))/(4pi epsilon_(0))]^(1//2)`

C

`(1)/(c^(2)) [(e^(2))/(G 4 pi epsilon_(0))]^(1//2)`

D

`(1)/(c)G(e^(2))/(4pi epsilon_(0))`

Text Solution

Verified by Experts

The correct Answer is:
A
As force `F = (e^(2))/(4pi epsilon_(0)r^(2)) rArr (e^(2))/(4pi epsilon_(0)) = r^(2)F`
Putting dimensions of r and F, we get
`rArr [(e^(2))/(4pi epsilon_(0))] = [ML^(3)T^(-2)]` ...(i)
Also, force, `F = (Gm^(2))/(r^(2))`
`rArr [G] = ([MLT^(-2)][L^(2)])/([M^(2)])`
`rArr [G] = [M^(-1)L^(3)T^(-2)]` ..(i)
and `[(1)/(c^(2))] = (1)/([L^(2)T^(-2)]) = [L^(-2)T^(2)]` ..(iii)
Now, checking optionwise,
`=(1)/(c^(2)) ((Ge^(2))/(4pi epsilon_(0)))^(1//2)`
`= [L^(-2)T^(2)] [L^(6)T^(-4)]^(1//2) = [L]`
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Knowledge Check

  • A physical quantity of the dimension of length that can be formed out of c, G and (e^2)/(4 pi epsilon_0) is [c is velocity ] of light G is universal constant of gravitation and c is charge.

    A
    `c^2 [C (e^2)/(4 pi epsilon_0]^(1//2)`
    B
    `1/(c^2) [(e^2)/(G 4 pi epsilon_0)]^(1//2)`
    C
    `1/(c^2) G (e^2)/(4 pi epsilon_0)`
    D
    `1/(c^2) [G (e^2)/(4 pi epsilon_0)]^(1//2)`

  • A physical quantity of the dimension of length that can be formed out of c, Gand (e^2)/(4pi epsilon_0) is (c is velocity of light , G is universal constant of gravitation and e is charge ]:

    A
    `c^2 [G (e^1)/(4 pi epsilon_0)]^(1//2)`
    B
    `1/(c^2) [(e^2)/(G 4 pi epsilon_0)]^(1//2)`
    C
    `1/(c^2) G (e^2)/(4 pi epsilon_0)`
    D
    `1/(c^2) [G (e^2)/(4 pi epsilon_0)]^(1//2)`

  • A physical quantity of the dimensions of length that can be formed out of c, G and e is [c is velocity of light, G is universal constant of gravitation and e is charge)

    A
    `c^(2)[G(e^(2))/(4piepsilon_(0))]^(1//2)`
    B
    `(1)/(c^(2))[(e^(2))/(G4piepsilon_(0))]^(1//2)`
    C
    `(1)/(c^(2))G(e^(2))/(4piepsilon_(0))`
    D
    `(1)/(c^(2))[G(e^(2))/(4piepsilon_(0))]^(1//2)`

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