The Question is from neet-chemistry , and it was created by the author THIRUPATHI REDDY

Question

Three forces $\vec{F_1} = 2\hat{i} - 3\hat{j}$, $\vec{F_2} = -5\hat{i} + \hat{j}$, and $\vec{F_3} = a\hat{i} + b\hat{j}$ act on a particle. If the particle is in equilibrium, the values of *a* and *b* are:

THIRUPATHI REDDY · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
	**Primary Concept**: Equilibrium of Forces
	**Related Topics**: Vector Addition, Newton's First Law
	**Prerequisites**: Understanding of vectors and equilibrium conditions.
## SOLUTION PATHWAY
**Given Information**:
	$\vec{F_1} = 2\hat{i} - 3\hat{j}$
	$\vec{F_2} = -5\hat{i} + \hat{j}$
	$\vec{F_3} = a\hat{i} + b\hat{j}$
	Particle is in equilibrium.
**Method & Steps**:
	1. **Condition for Equilibrium**: For a particle to be in equilibrium, the vector sum of all forces acting on it must be zero.
		Reasoning: Newton's First Law states that an object at rest stays at rest unless acted upon by a net force.  In equilibrium, the net force is zero.
		Formula/Rule: $\vec{F_1} + \vec{F_2} + \vec{F_3} = 0$
	2. **Vector Sum**: Add the given force vectors.
		Working: $(2\hat{i} - 3\hat{j}) + (-5\hat{i} + \hat{j}) + (a\hat{i} + b\hat{j}) = (2 - 5 + a)\hat{i} + (-3 + 1 + b)\hat{j} = 0$
		Key Point:  The zero vector is represented as $0\hat{i} + 0\hat{j}$.
	3. **Solve for *a* and *b***:
		Result: $(-3 + a)\hat{i} + (-2 + b)\hat{j} = 0\hat{i} + 0\hat{j}$. This implies $-3 + a = 0$ and $-2 + b = 0$. Therefore, $a = 3$ and $b = 2$.
		Verification: Substituting $a = 3$ and $b = 2$ into the vector sum confirms that the net force is zero.
## OPTION ANALYSIS
[A] ✓: $a = 3, b = 2$. This is the correct answer, as derived above.
[B] :x: $a = -3, b = -2$. This would result in a net force of $-6\hat{i} - 4\hat{j}$, which is not zero.
[C] :x: $a = 2, b = 3$. This would result in a net force of $-1\hat{i} + \hat{j}$, which is not zero.
[D] :x: $a = -2, b = -3$. This would result in a net force of $-5\hat{i} - 5\hat{j}$, which is not zero.
## LEARNING AIDS
	**Common Mistakes**:
		1. Incorrectly adding the vector components: Ensure proper addition of the *i* and *j* components separately.
		2. Misinterpreting the equilibrium condition: Remember that equilibrium implies a net force of zero.
	**Quick Tips**:
		1. Treat the *i* and *j* components independently when adding vectors.
		2.  Visualize the vectors graphically to confirm that their sum results in a zero vector for equilibrium.

THIRUPATHI REDDY · Answer

The correct Option is "a = 3, b = 2"

THIRUPATHI REDDY · Answer

a = -3, b = -2

THIRUPATHI REDDY · Answer

a = 2, b = 3

THIRUPATHI REDDY · Answer

a = -2, b = -3

NEET Chemistry MCQs

Select Chapter

Question Tags

Question Tags

NEET Subjects

Our Bots

Company