Question

Three particles each of mass 1 kg are placed at the corners of a right angled triangle AOB, O being the origin of the coordinate system (OA and OB along positive X- direction and positive Y- direction). If OA=OB=1m, the positive vector of the centre of mass (in metres) is:

• A. $ \frac{\widehat{i}+\widehat{j}}{3} $
• B. $ \frac{2\left( \widehat{i}+\widehat{j} \right)}{3} $
• C. $ \frac{2\left( \widehat{i}-\widehat{j} \right)}{3} $
• D. $ \left( \widehat{i}-\widehat{j} \right) $

Answer 1

The Correct Option is A

Three particles each of mass 1 kg are placed the three corners of a right angled triangle. Here, $ {{m}_{1}}={{m}_{2}}={{m}_{3}}=1 $ $ ({{x}_{1}},{{y}_{1}})=(0,0) $ $ ({{x}_{3}},{{y}_{3}})=(0,1) $ $ ({{x}_{CM}},{{y}_{CM}})=? $ $ {{x}_{CM}}=\frac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}+{{m}_{3}}{{x}_{3}}}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}} $ $ {{x}_{CM}}=\frac{1.0+1.1+1.0}{1+1+1} $ $ {{x}_{CM}}=\frac{1}{3} $ $ {{y}_{CM}}=\frac{{{m}_{1}}{{y}_{1}}+{{m}_{2}}{{y}_{2}}+{{m}_{3}}{{y}_{3}}}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}} $ $ {{y}_{CM}}=\frac{1.0+1.0+1.1}{1+1+1} $ $ {{y}_{CM}}=\frac{1}{3} $ $ \therefore $ $ \vec{r}\,CM={{x}_{CM}}\hat{i}+{{y}_{CM}}\hat{j}=\frac{1}{3}\hat{i}+\frac{1}{3}\hat{j} $ $ {{\vec{r}}_{CM}}=\frac{\hat{i}+\hat{j}}{3} $