NEET-XII-Physics

exam-2 year:2016

with Solutions - page 2
  • #113
    Planck'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:   3
    Ans : (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;    =  