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 =