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Two objects of mass \mathrm{10kg} and \mathrm{20kg} respectively are connected to the two ends of a rigid rod of length \mathrm{10m} with negligible mass. The distance of the centre of mass system from the \mathrm{10kg} mass is :

Option: 1

\mathrm{\frac{20}{3}m}


Option: 2

\mathrm{10m}


Option: 3

\mathrm{5m}


Option: 4

\mathrm{\frac{10}{3}m}


Answers (1)

best_answer

Let the com be at the origin

\mathrm{r_{c m} =\frac{m_{1}r_{1}+m_{2} r_{2}}{m_{1}+m_{2}}} \\

\mathrm{0 =\frac{20\left(r_{1}\right)+10\left(-r_{2}\right)}{30} }

\mathrm{r_{1}=\frac{r_{2}}{2} \qquad\rightarrow 1} \\

\mathrm{\because r_{1}+r_{2}=10 \mathrm{~m} \text { (given) }} \\

\mathrm{\therefore r_{1}=\frac{10}{3} \mathrm{~m}} \\

\mathrm{r_{2}=\frac{20}{3} \mathrm{~m}}

the distance of the centre of mass of the system from the 10kg mass is  \mathrm{r_{2}=\frac{20}{3} m} \\

Hence the correct option is 1

Posted by

Deependra Verma

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