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

Question

Question

This question was previously asked in

SSC GD Constable 2025 Official Paper (Held On: 04 Feb, 2025 Shift 3)

Answer 1

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.