A boat of area 10 m^2 floating on the surface of a river is...

A boat of area $10 \mathrm{~m}^{2}$ floating on the surface of a river is made to move horizontally with a speed of $2 \mathrm{~ms}^{-1}$ by applying a tangential force. If the river is $1 \mathrm{~m}$ deep and the water in contact with the bed is stationary, what is the tangential force needed to keep the boat moving? (viscosity of water $0.01$ poise) (A) $0.04 \mathrm{~N}$ (B) $0.05 \mathrm{~N}$ (C) $0.02 \mathrm{~N}$ (D) $0.03 \mathrm{~N}$

A boat of area $10 \mathrm{~m}^{2}$ floating on the surface of a river is made to move horizontally with a speed of $2 \mathrm{~ms}^{-1}$ by applying a tangential force. If the river is $1 \mathrm{~m}$ deep and the water in contact with the bed is stationary, what is the tangential force needed to keep the boat moving? (viscosity of water $0.01$ poise)
(A) $0.04 \mathrm{~N}$
(B) $0.05 \mathrm{~N}$
(C) $0.02 \mathrm{~N}$
(D) $0.03 \mathrm{~N}$

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Key Concepts

Viscosity

Viscosity refers to a fluid's inherent resistance to flow or deformation under shear stress. In a Newtonian fluid, this resistance is quantified by a constant which relates the shear stress to the rate at which adjacent layers of fluid move relative to each other.

Newton's Law of Viscosity

Newton's Law of Viscosity expresses the relationship between shear stress and the velocity gradient in a fluid. It states that the shear stress is directly proportional to the velocity gradient, with viscosity serving as the proportionality constant, making it key in analyzing forces in moving and stationary fluids.

Shear Stress

Shear stress is defined as the force per unit area exerted parallel to the surface of an object in a fluid medium. It arises when layers of the fluid, moving at different speeds, act on surfaces in contact with them, and is calculated as the product of viscosity and the velocity gradient.

Drag Force due to Viscosity

The drag force due to viscosity is the resistive force that must be overcome to maintain motion through a viscous fluid. This force is computed by integrating the shear stress over the area of the object in contact with the fluid, and it plays a critical role in determining the net force required to sustain steady motion.

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