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 =