Question

For a book of mass m, moving a distance d on a smooth horizontal table, the work done due gravitational force is:

• A. md
• B. mgd
• C. 0
• D. m d cos θ

Answer 1

Answer:

C. 0

Understanding Work Done by Gravitational Force

Definition of Work

• Work done in physics is defined as the product of the force applied to an object and the distance moved in the direction of the force. Mathematically, Work (W) = Force (F) × distance (d) × cos(θ), where θ is the angle between the force and the displacement vector.

• For work to be done, there must be both a force and a displacement. Crucially, the displacement must have a component in the direction of the applied force.

Gravitational Force and Horizontal Motion

• Gravitational force acts vertically downwards on an object. On Earth, this force is equal to the object's weight (W = mg), where 'm' is the mass and 'g' is the acceleration due to gravity.

• In the given scenario, the book is moving on a smooth horizontal table. This means the displacement is purely horizontal.

• The gravitational force is acting vertically downwards, and the displacement is horizontal. Therefore, the angle (θ) between the gravitational force and the direction of motion is 90 degrees.

Calculating Work Done

• Using the work formula: W = F × d × cos(θ)

• Here, F is the gravitational force (mg), d is the horizontal distance moved.

• The angle θ = 90 degrees.

• The value of cos(90°) is 0.

• Therefore, Work done by gravitational force = mg × d × cos(90°) = mg × d × 0 = 0 Joules.