Wheatstone's Bridge - 4

The value of the unknown resistance lies in-between 16.38 and 16.39 .
The unknown vaalue may be the average of the two
i.e. X = = 16.385

Problems:
Easy:

1. E, m, J and G denote energy, mass, angular momentum and gravitational constant respectively. Then the dimensions of EJ²/m⁵G² are:
   Solution:- E is [ML²L^-2]      m is [ML⁰T⁰]
   angular momentum is product of linear momentum with distance
   J is [ML₂T^-1]
   for G
   
   dimensionally G = = [M^-1L³T^-2]
   Now, = [M^{1 + 2 - 5 + 2}L^{2 + 4 - 6}T^{- 2 - 2 + 4}]
                          = [M⁰L⁰T⁰]
   
   
2. The equation of state of some gases can be expressed as (v - b) = RT
   where P pressure.
   v volume.
   T absolute temp.
   then the dimension of ‘a’ are:-
   Solution:- Physical quantities with same dimensions can only be added or subtracted.
   dimensions of must be same as that of P = F/A
                                                                            = [MLT^-2]/[L²]
                                                                            = [ML^-1T^-2]
   = [ML^-1T^-2]
   a = [ML⁵T^-2]
   
   
3. The percentage error in the measurement of a physical quantity m given by m = K tan where K is a constant. For what value of is the percentage error minimum ?
   Solution:- Since m = K tan
   differentiating
       
   % error =