1- Force of viscosity F acting on a spherical body moving through a fluiddepends upon its velocity (v), radius (r) and coefficient of viscosity ‘η’ ofthe fluid. Using method of dimensions obtain an expression for ‘F’.

To obtain an expression for the force of viscosity (F) acting on a spherical body moving through a fluid, we can use the method of dimensions.

Step 1: Identify the variables involved in the problem. In this case, we have:

• Force of viscosity (F)
• Velocity of the body (v)
• Radius of the body (r)
• Coefficient of viscosity of the fluid (η)

Step 2: Determine the dimensions of each variable. The dimensions are represented by square brackets. For example, the dimension of velocity is [L/T] (length per time), the dimension of radius is [L] (length), and the dimension of coefficient of viscosity is [M/LT] (mass per length per time).

Step 3: Write the equation using the dimensions of the variables. The force of viscosity can be expressed as: F = k * v^a * r^b * η^c

Step 4: Determine the exponents (a, b, c) and the constant (k) by equating the dimensions on both sides of the equation.

• Equating the dimensions of force on both sides, we have: [M L T^-2] = [M^a L^a T^-a] * [L^b] * [M L^-1 T^-1]^c

• Equating the dimensions of mass on both sides, we have: 1 = a + c

• Equating the dimensions of length on both sides, we have: 0 = a + b

• Equating the dimensions of time on both sides, we have: -2 = -a - c

Solving these equations simultaneously, we find: a = 1 b = -1 c = 0

Therefore, the expression for the force of viscosity (F) is: F = k * v * r^-1 * η^0 F = k * v * r^-1

Note: The coefficient of viscosity (η) does not affect the force of viscosity in this case.