Question

As shown in figure from a uniform rectangular sheet a triangular sheet is removed from one edge. The shift of centre of mass is

• A. 4.2 cm
• B. -4.2cm
• C. 6.67 cm
• D. -6.67 cm

Answer 1

The correct option is D

-6.67 cm

The shift in centre of mass

$x_m$ = $\frac{m_1{x}_1-m_2{x}_2}{m_1-m_2}$

Where $x_1=Distanceofcentreofmassofwholesheetfro{m}^{\prime }{O}^{\prime }\Rightarrow x_1=0$

Where $x_2=Distanceofcentreofmassofremovedportionfro{m}^{\prime }{O}^{\prime }\Rightarrow x_2=OC=20cm$

And $m_1=\sigma (20\times 60);m_2=\sigma \frac{1}{2}\left(20\right)\left(30\right)$

$\therefore$ $x_{cm}$=$\frac{\sigma (20\times 60)\left(0\right)-\sigma \frac{1}{2}\left(20\right)\left(30\right)\left(20\right)}{\sigma (20\times 60)-\sigma \frac{1}{2}\left(20\right)\left(30\right)}$

$\Rightarrow x_{cm}$ = -6.67cm