Question

A rod of length 2 l is bent as shown in figure, coordinates of center of mass are:

• A. $(\frac{2l}{3},\frac{l}{3})$
• B. $(\frac{l}{8},\frac{l}{8})$
• C. $(\frac{l}{4},\frac{3l}{4})$
• D. $(\frac{l}{3},\frac{l}{6})$

Answer 1

The correct option is C $(\frac{l}{4},\frac{3l}{4})$

The system can be treated as two separate rods of length $\ell$ each, let their mass per unit length be $\lambda$.

$x_{CM}=\frac{\left(\lambda \ell \right)\left(0\right)+\lambda \left(\frac{\ell }{2}\right)\ell }{2\lambda \ell }$

$=\frac{\ell }{4},ycm=\frac{3l}{4}$ ( similarly)

$\Rightarrow$ co-ordinates of $CM$ are $(\frac{\ell }{4},\frac{3l}{4})$