Question

A metal plate of area 10^-2m² rests on a layer of castor oil, 2 × 10^-3m thick, whose viscosity coefficient is 1.55 Ns/m². The approximate horizontal force required to move the plate with a uniform speed of 3 × 10^-2ms^-1 is:

• A. 0.6718 N
• B. 0.2325 N
• C. 0.2022 N
• D. 0.6615 N

Hint:

To calculate the force required to move a plate through a viscous fluid, use the equation for viscous force, which includes the coefficient of viscosity, the area of the plate, and the velocity divided by the fluid thickness

Answer 1

The Correct Option is B

Calculating the Force Required to Move a Plate:

1. Step 1: The force required to move the plate is given by the formula for viscous force:
   \[ F = \eta \cdot A \cdot \frac{v}{d} \] where:
   • \( \eta \) is the coefficient of viscosity
   • \( A \) is the area of the plate
   • \( v \) is the velocity
   • \( d \) is the thickness of the fluid
2. Step 2: Substituting the given values into the formula:
   \[ F = (1.55 \, \text{Ns/m}^2) \cdot (10^{-2} \, \text{m}^2) \cdot \frac{3 \times 10^{-2} \, \text{m/s}}{2 \times 10^{-3} \, \text{m}} \] Simplifying:
   \[ F = 1.55 \cdot 10^{-2} \cdot \frac{3 \times 10^{-2}}{2 \times 10^{-3}} \] \[ F = 1.55 \cdot 10^{-2} \cdot 15 = 0.2325 \, \text{N} \]

Final Answer: The force required to move the plate is \( F = 0.2325 \, \text{N} \).

Answer 2

Correct Option: Option 2

Given values:

• Area of the plate (A) = 10^-2 m²
• Thickness of the castor oil layer (dx) = 2 × 10^-3 m
• Coefficient of viscosity (η) = 1.55 Ns/m²
• Uniform speed of the plate (dv) = 3 × 10^-2 ms^-1

Formula for viscous force:

F = ηA (dv/dx)

Calculation of velocity gradient:

dv/dx = (3 × 10^-2 ms^-1) / (2 × 10^-3 m) = 15 s^-1

Calculation of viscous force:

F = (1.55 Ns/m²) × (10^-2 m²) × (15 s^-1)

F = 1.55 × 10^-2 × 15 N

F = 23.25 × 10^-2 N

F = 0.2325 N

Answer: The approximate horizontal force required is 0.2325 N.