question_answer

A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be :- [JEE Main 8-4-2019 Afternoon]

A) \[\left( \frac{2a}{3},\frac{2b}{3} \right)\]                  

B) \[\left( \frac{5a}{3},\frac{5b}{3} \right)\]

C) \[\left( \frac{3a}{4},\frac{3b}{4} \right)\]      

D)   \[\left( \frac{5a}{12},\frac{5b}{12} \right)\]

Correct Answer: D

Solution :

\[x=\frac{M\frac{a}{2}-\frac{M}{4}\times \frac{3a}{4}}{M-\frac{M}{4}}\]             \[=\frac{\frac{a}{2}-\frac{3a}{16}}{\frac{3}{4}}=\frac{\frac{5a}{16}}{\frac{3}{4}}=\frac{5a}{12}\]             \[y=\frac{M\frac{b}{2}-\frac{M}{4}\times \frac{3b}{4}}{M-\frac{M}{4}}=\frac{5b}{12}\]