Wheatstone's Bridge - 5

obvisously percentage error is minimum when sin2 is maximum.
20 =
or

4. The value of a force on a body is 20N is SI units. What is the value of this force in CGS units, that is dynes ?
Solution:- Dimensions of force = MLT^-2
Unit of force in Si = Kg m/S²
    Unit of force in CGs = g cm/S²
Let n be the numerical value of force in CGS system.
20 Kg m/S² = n g cm/S²
n =
       = 20 x 10⁵
20 N = 2 x 10⁶ dynes

5. Assuming that the critical velocity of flow of a liquid through a narrow tube depends on the radius of the tube, density of the liquid and viscosity of the liquid, find the expression for critical velocity.
Solution:- Suppose v = K r^ap^bc
where r = radius of the tube,      p = density of liquid
          = coefficient of viscosity of the liquid      K dimensionless constant
dimensional equation will be
[LT^-1] = [L}^a[ML^-3]^b[ML^-1T^-1]^c
[LT^-1] = [M^{b + c}L^{a - 3b - c} T^-c]
fro equivalence
b + c = 0
a - 3b - c = 1
also   - c = - 1        => c = 1
         b = - c = - 1
         a = 3b + c + 1 = - 3 + 1 + 1 = - 1
v = K r^-1p^-1
    v =