Question

A uniform rod of length 2l is bent in the shape of letter l . coordination of its centre of mass are

Answer 1

Answer: The coordinates of its center of mass are $\dfrac{l}{2}, \dfrac{l}{2}$.

Explanation:

Given that,

Length of the rod = 2l

After bent in the shape of letter l , the length of the each side of the rod is l.

Coordinate of along x-axis = l,0

Coordinate of along y-axis = 0,l

Now, Coordinates of center of mass of both axis

Coordinates of center of mass along x-axis

$X_{cm} = \dfrac{m_{1}x_{1}+ m_{2}x_{2}}{m_{1}+m_{2}}$

$X_{cm} = \dfrac{ml+0}{2m}$

$X_{cm} = \dfrac{l}{2}$

Coordinates of center of mass along y-axis

$Y_{cm} = \dfrac{m_{1}y_{1}+ m_{2}y_{2}}{m_{1}+m_{2}}$

$Y_{cm} = \dfrac{0+ml}{2m}$

$Y_{cm} = \dfrac{l}{2}$

Hence, the coordinates of its center of mass are $\dfrac{l}{2}, \dfrac{l}{2}$.

Answer 2

"Given the length of the rod is 2l

If the rod is bent into ‘L’ shape. then the length of the rod on each side is l.

Let us consider the coordinates along x-axis is l, 0

The coordinates along y-axis is 0, l

Consider the coordinates of centre of mass along x-axis is

${ X }_{ cm }\quad =\quad m1z1+\frac { m2z2 }{ m1 } +m2$

${ X }_{ cm }\quad =\quad ml+\frac { 0 }{ 2 } m\quad =\quad \frac { 1 }{ 2 }$

Consider the coordinates of centre of mass along y-axis is

${ Y }_{ cm }\quad =\quad m1y1+\frac { m2y2 }{ m1 } +m2$

${ Y }_{ cm }\quad =\quad 0+\frac { m1 }{ 2m } \quad =\quad \frac { l }{ 2 }$

Therefore the coordinates of the centre of mass are $\frac { 1 }{ 2 } ,\frac { 1 }{ 2 }$"