question_answer

The U shaped object shown in the figure has outside dimensions of 100 mm each side and each of its three sides is 20 mm wide. The respective values of the X, Y and Z coordinates of the center of mass of the object will be close to

A)  (50, 50, 3) mm                 

B)  (50, 50, 6) mm

C)  (50, 38, 3) mm                 

D)  (50, 41, 3) mm

Correct Answer: D

Solution :

                 COM is exactly halfway from other end

Object	Mean	x	y	z
Left bar	\[{{m}_{A}}\]	10mm	50mm	3mm
Right bar	\[{{m}_{B}}\]	90mm	50 mm	3mm
Bottom bar	\[{{m}_{C}}\]	50 mm	50 mm	3 mm

                                \[{{x}_{\min }}=\frac{{{m}_{A}}{{x}_{A}}+{{m}_{B}}+{{x}_{B}}+{{m}_{c}}{{x}_{c}}}{{{m}_{sys}}}\]                                 \[=\frac{m\,(10)+m\,(90)+0.6\,m(50)}{2.6\,m}\]\[=50\,mm\]                                     \[{{y}_{\min }}=\frac{{{m}_{A}}{{V}_{A}}+{{m}_{B}}{{y}_{B}}+{{m}_{c}}\,{{y}_{c}}}{{{m}_{sys}}}\]                                 \[=\frac{m\,(50)+m\,(50)+0.6\,m\,(10)}{2.6\,m}41\,mm\]                               \[z=\frac{m\,(3\,mm)+m(3\,mm)+0.6\,m\,(3\,mm)}{2.6\,m}\]\[z=3\ mm\]