A force of 8 N acts on an object of mass 5 kg in X -direction and another force of 6 N acts o

Step 1: We are given that a force of $8 mathrm{~N}$ acts on an object of mass $5 mathrm{~kg}$ in

A force of 8 N acts on an object of mass 5 kg in X...

A force of $8 \mathrm{~N}$ acts on an object of mass $5 \mathrm{~kg}$ in $\mathrm{X}$ -direction and another force of $6 \mathrm{~N}$ acts on it in $\mathrm{Y}$ -direction. Hence, the magnitude of acceleration of object will be (A) $1.5 \mathrm{~ms}^{-2}$ (B) $2.0 \mathrm{~ms}^{-2}$ (C) $2.5 \mathrm{~ms}^{-2}$ (D) $3.5 \mathrm{~ms}^{-2}$

A force of $8 \mathrm{~N}$ acts on an object of mass $5 \mathrm{~kg}$ in $\mathrm{X}$ -direction and another force of $6 \mathrm{~N}$ acts on it in $\mathrm{Y}$ -direction. Hence, the magnitude of acceleration of object will be
(A) $1.5 \mathrm{~ms}^{-2}$
(B) $2.0 \mathrm{~ms}^{-2}$ (C) $2.5 \mathrm{~ms}^{-2}$
(D) $3.5 \mathrm{~ms}^{-2}$

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Key Concepts

Newton's Second Law of Motion

This principle states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass. Mathematically, it is expressed as F = ma, where F is the net force, m is the object's mass, and a is the acceleration. In problems involving forces, this law is crucial for determining how forces affect an object's motion.

Vector Addition of Forces

Since forces are vector quantities, they possess both magnitude and direction. When multiple forces act on an object, their net effect is found by vector addition. This means that forces acting in perpendicular directions are combined by treating them as components, which is essential for accurately determining the resultant force that governs the object's acceleration.

Pythagorean Theorem in Vector Components

When forces act along perpendicular axes, the magnitude of the resultant force is found by using the Pythagorean theorem. This involves squaring the individual force components, summing these squares, and taking the square root of the result. This approach simplifies the process of calculating the resultant force magnitude when dealing with orthogonal components.

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