A particle of mass 100 g is thrown vertically upwards with a speed of 5 m / s. The work done b

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A particle of mass 100 g is thrown vertically upwards with...

A particle of mass $100 \mathrm{~g}$ is thrown vertically upwards with a speed of $5 \mathrm{~m} / \mathrm{s}$. The work done by the force of gravity during the time the particle goes up is [2006] (A) $-0.5 \mathrm{~J}$ (B) $-1.25 \mathrm{~J}$ (C) $1.25 \mathrm{~J}$ (D) $0.5 \mathrm{~J}$

A particle of mass $100 \mathrm{~g}$ is thrown vertically upwards with a speed of $5 \mathrm{~m} / \mathrm{s}$. The work done by the force of gravity during the time the particle goes up is [2006]
(A) $-0.5 \mathrm{~J}$
(B) $-1.25 \mathrm{~J}$
(C) $1.25 \mathrm{~J}$
(D) $0.5 \mathrm{~J}$

Key Concepts

Work-Energy Theorem

The work-energy theorem connects the concepts of work and kinetic energy, stating that the net work done on an object is equal to its change in kinetic energy. This theorem is instrumental in analyzing the motion of particles, as it allows one to relate the work performed by forces (including gravity) to changes in the object's speed or kinetic energy, thus linking force, displacement, and energy.

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. As an object moves upward against the gravitational force, its potential energy increases while the work done by gravity is negative, indicating that gravity is doing work against the motion. This concept is central to understanding energy conservation in systems where gravity is a key force.

Work Done by a Force

This concept refers to the process of calculating the work performed when a force is applied over a displacement. The work is mathematically defined as the dot product of force and displacement vectors. It takes into account both the magnitude of the force and the direction of both the force and the displacement, meaning that the work done can be positive, negative, or zero depending on the relative orientation of these vectors.

Gravitational Force

Gravitational force is the attractive force exerted by the Earth on objects within its vicinity. It is a constant force near the Earth’s surface and acts in the downward direction. When an object moves in the gravitational field, the work done by gravity depends on the displacement relative to the direction of gravity, which plays a key role in energy transfer in many mechanical processes.

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