A force (3 î-2 ĵ) N acting on a particle, does zero work...

A force $(3 \hat{i}-2 \hat{j}) \mathrm{N}$ acting on a particle, does zero work when the particle is displaced from point $(1,-1)$ to a point $(2, a)$. Then a is (position co-ordinates are in metre) (a) $\frac{1}{2} \mathrm{~m}$ (b) $1 \mathrm{~m}$ (c) $\frac{3}{2} \mathrm{~m}$ (d) $-\frac{3}{2}$

A force $(3 \hat{i}-2 \hat{j}) \mathrm{N}$ acting on a particle, does zero work when the particle is displaced from point $(1,-1)$ to a point $(2, a)$. Then a is (position co-ordinates are in metre)
(a) $\frac{1}{2} \mathrm{~m}$
(b) $1 \mathrm{~m}$
(c) $\frac{3}{2} \mathrm{~m}$
(d) $-\frac{3}{2}$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Work

Work in physics is defined as the scalar product (dot product) of the force vector and the displacement vector. It represents the energy transferred by a force acting through a displacement, and when the dot product is zero, it indicates that no energy is transferred, typically because the force is perpendicular to the displacement.

Dot Product

The dot product is a mathematical operation that takes two vectors and returns a scalar quantity. It is calculated by multiplying the corresponding components of the vectors and summing these products. A zero dot product indicates that the two vectors are orthogonal, meaning they are at right angles to each other.

Displacement Vector

The displacement vector represents the change in position of an object between its initial and final positions. It is determined by subtracting the initial coordinates from the final coordinates. In the context of work, the displacement vector is used in conjunction with the force vector to determine if work is done through their dot product.

Transcript

Please give Ace some feedback