Composite & Cut-Out Bodies question from JEE Main 2019 (12 Jan, Shift 1)

Answer: (c)

1. The bar has three straight parts (the left vertical line is the y-axis, not the bar); mass $\propto$ length.
2. Top part: length $2L$, centre $(L,\ L)$. Vertical part: length $L$, centre $(2L,\ L/2)$. Bottom part: length $L$, centre $(2.5L,\ 0)$.
3. Total length $4L$: $x_{cm} = \frac{2L(L)+L(2L)+L(2.5L)}{4L} = \frac{13}{8}L$
4. $y_{cm} = \frac{2L(L)+L(L/2)+L(0)}{4L} = \frac{5}{8}L$
5. So the answer is (c) $\vec{r}_{cm} = \frac{13}{8}L\,\hat{x} + \frac{5}{8}L\,\hat{y}$.