Question 1) An equilaterat triangte ptate with sides \( a \) and muss \( 4 \mathrm{~m} \) is placed as shown in the figure. First, a point object with mass \( 4 \mathrm{~m} \) is placed in vertex. \( P \) of the plate, and then a point object with mass \( 4 \mathrm{~m} \) is removed and a point objeot with mass \( m \) is placed in vertex \( Q \). In both cases, the \( x \)-coordinate of the center of mass of the mass system is the same. Find the center of mass \( x_{C M} \) of the triangular plate? \( \frac{a}{6} \) B) \( \frac{a}{3} \) C) \( \frac{6 a}{3} \) D) \( \frac{2 a}{3} \) E) \( \frac{3 a}{2} \)