Question

A particle is moved along the different paths $OAC, OBC, ODC$ and $OEC$ as shown in the figure. Path $ODC$ is a parabola, $y=4x^2$ and path $OEC$ is a straight line, $(y=2x)$. Find the work done by a force $\overrightarrow{F} = xy\hat{i} + x^2y\hat{j}$ on the particle along these paths.

• A. P-4; Q-3; R-2; S-1
• B. P-4; Q-2; R-3; S-1
• C. P-4; Q-3; R-1; S-2
• D. P-3; Q-4; R-1; S-4

Answer 1

Answer: (A)

P-4; Q-3; R-2; S-1

Answer 2

1. For path OAC, work is calculated by adding 0 (along OA) and 8 (along AC) → 8 J.
2. For path OBC, work is 0 (along OB) + 2 (along BC) → 2 J.
3. For path ODC, parameterize $y=4x^2$ and integrate to get $\frac{19}{3}$ J.
4. For path OEC, parameterize $y=2x$ to get $\frac{5}{3}$ J.
5. Matching these with List–II gives: P → 4, Q → 3, R → 2, S → 1.