With two forces acting at a point, the maximum effect is obtained when their resultant is 4 N. If they act at right angles, then their resultant is 3 - Mathematics MCQ AIEEE 2004 2026 | ExamTest.live

hardMCQAIEEE 20042026Mathematics

1 attempts0% success rate3 marks (−1)

With two forces acting at a point, the maximum effect is obtained when their resultant is 4 N . If they act at right angles, then their resultant is 3 N . Then the forces are

Solution & Step-by-step Explanation

Let the two forces be P and Q . The maximum resultant is when they are in the same direction: P + Q = 4 . When acting at right angles, the resultant is P^{2} + Q^{2} = 3 \Rightarrow P^{2} + Q^{2} = 9 . We have (P + Q)^{2} = P^{2} + Q^{2} + 2 PQ . 4^{2} = 9 + 2 PQ \Rightarrow 16 - 9 = 2 PQ \Rightarrow 2 PQ = 7 \Rightarrow PQ = 3.5 . Also (P - Q)^{2} = P^{2} + Q^{2} - 2 PQ = 9 - 7 = 2 \Rightarrow P - Q = 2 . Solving P + Q = 4 and P - Q = 2 : 2 P = 4 + 2 \Rightarrow P = 2 + \frac{2}{2} = 2 + \frac{1}{2} . Wait, let's check the options. P = 2 + \frac{1}{2} 2 and Q = 2 - \frac{1}{2} 2 . Indeed, (2 + \frac{2}{2}) + (2 - \frac{2}{2}) = 4 . (2 + \frac{2}{2})^{2} + (2 - \frac{2}{2})^{2} = (4 + \frac{1}{2} + 22) + (4 + \frac{1}{2} - 22) = 9 .

Try it yourself before checking the explanation above.

With two forces acting at a point, the maximum effect is obtained when their resultant is 4 N . If they act at right angles, then their resultant is 3 N . Then the forces are

(2 + 2) N and (2 - 2) N

(2 + 3) N and (2 - 3) N

(2 + \frac{1}{2} 2) N and (2 - \frac{1}{2} 2) N

(2 + \frac{1}{2} 3) N and (2 - \frac{1}{2} 3) N

Practice with timed mock tests and track your performance across Mathematics.