Question

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:
(A) (5a/3, 5b/3)
(B) (2a/3, 2b/3)
(C) (3a/4, 3b/4)
(D) (5a/12, 5b/12)

Answer 1

$\huge\bold{(A)}$

(5a/3.5b/3)

Answer 2

The coordinates of the centre of mass of the remaining portion will be x =  5 a /12 and y =  5 b / 12

Option (D) is correct.

Explanation:

x = M (a/2) - M /4 x 3a / 4 ÷ M - M / 4

x = a/2 - 3a / 16 ÷ 3 / 4 = 16 ÷ 3/4 = 5 a /12

y = M b / 2 - M / 4 x 3b /4  ÷  M - M / 4 = 5 b / 12

Thus the coordinates of the centre of mass of the remaining portion will be

x =  5 a /12 and y =  5 b / 12