A large wooden plate of area `10m^2` floating on the surface of river is made to move horizontally with a speed of `2ms^-1` by applying a tangential force. If the river is 1m deep and the water in contact with the bed is stationary, find the tangential force needed to keep the plate moving. Coefficient of viscosity of water at the temperature of the river `=10^-2 poise.`

Explanation

To solve the problem, we need to determine the tangential force required to keep the wooden plate moving at a constant speed in the water. We will use the concept of viscosity and the formula for viscous force.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Area of the plate, \( A = 10 \, m^2 \)
- Speed of the plate, \( v = 2 \, m/s \)
- Depth of the river, \( d = 1 \, m \) (this indicates the distance over which the velocity changes)
...