Vector Algebra
Applications of Vectors
Grade 12
Question:
<p>The horizontal force and the force inclined at an angle 60° with the vertical, whose resultant is in vertical direction of P kg, are</p>
<p>(a) P, 2P</p>
<p>(b) P, \(P\sqrt{3}\)</p>
<p>(c) 2P, \(P\sqrt{3}\)</p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: Resolve forces into components and use the condition that the horizontal resultant is zero while vertical resultant is P.
Let the horizontal force be F_1 and inclined force be F_2. The inclined force makes 60° with vertical, so 30° with horizontal. For the resultant to be vertical: F_1 = F_2 cos(30°) = F_2 · (√3/2). Also, the vertical component equals P: F_2 sin(30°) = P, so F_2 = 2P. Thus F_1 = 2P · (√3/2) = P√3.
Correct Answer: B