NEET-XII-Physics
exam-2 year:2016
- #113Planck's constant (h), speed of light in vacuum
and Newton's gravitational constant (G) are three
fundamental constants. Which of the following
combinations of these has the dimension of length?
(1)``\sqrt \frac {hc}{(G)}``
(2) ``\sqrt \frac {Gc}{(h^\frac 32)}``
(3) ``\sqrt \frac {Gh}{(c^\frac 32)}``
(4)``\sqrt \frac {Gh}{(c^\frac 52)}``digAnsr: 3Ans : (3)
Sol. x y zh G c
M0L1T0 = (ML2T-1)x (M-1L3T-2)y (LT-1)z
= Mx-y L2x+3y+z T-x-2y-z
Equating :
3/ 2
1 1 3
x y 0 x ;y ;z
2 2 2
2x 3y z 1
hG
x 2y z 0
c
= &implies; = = =
+ + =
&implies; =