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

The correct answer is 0.

Key Points

• The work done by a force is defined as the dot product of the force and the displacement in the direction of the force.
• On a smooth horizontal table, the gravitational force acts vertically downward, while the displacement is horizontal.
• The angle between the gravitational force and the horizontal displacement is 90 degrees.
• The cosine of 90 degrees is 0, hence the work done by the gravitational force over the horizontal displacement is zero.

Additional Information

• Work: In physics, work is done when a force acts upon an object to cause a displacement. It is calculated as the product of the force and the displacement in the direction of the force.
• Gravitational Force: The force of attraction between two masses. Near the Earth's surface, it imparts an acceleration of 9.81 m/s² downward.
• Dot Product: A mathematical operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number. It is defined as the product of the magnitudes of the two vectors and the cosine of the angle between them.
• Cosine Function: In trigonometry, the cosine of an angle in a right-angled triangle is the ratio of the length of the adjacent side to the length of the hypotenuse. The cosine of 90 degrees is 0.
• Smooth Surface: A surface with no friction. On a smooth horizontal table, there is no resistance to horizontal motion, and thus gravitational force does not affect horizontal displacement.