Figure shows a composite system of two uniform rods of lengths as indicated. Then the coordinates of the centre of mass of the system of rods are

Question

Figure shows a composite system of two uniform rods of lengths as indicated. Then the coordinates of the centre of mass of the system of rods are (A) ((L/2), (2 L/3)) (B) ((L/4), (2 L/3)) (C) ((L/6), (2 L/3)) (D) ((L/6), (L/3))

Tardigrade Admin · Accepted Answer

Centre of mass of the uniform rod will lie at its centre x cm =(m1 x1+m2 x2/m1+m2) x cm =(m((L/2))+2 m(0)/3 m), yc m=(2 m(L)+m(0)/3 m) x cm =(L/6), y cm =(2 L/3)

Q. Figure shows a composite system of two uniform rods of lengths as indicated. Then the coordinates of the centre of mass of the system of rods are

$(\frac{L}{2}, \frac{2 L}{3})$

$(\frac{L}{4}, \frac{2 L}{3})$

$(\frac{L}{6}, \frac{2 L}{3})$

$(\frac{L}{6}, \frac{L}{3})$

Centre of mass of the uniform rod will lie at its centre
$x_{c m} = \frac{m _{1} x _{1} + m _{2} x _{2}}{m _{1} + m _{2}}$
$x_{c m} = \frac{m ( \frac{L}{2} ) + 2 m ( 0 )}{3 m}, y_{c m} = \frac{2 m ( L ) + m ( 0 )}{3 m}$
$x_{c m} = \frac{L}{6}, y_{c m} = \frac{2 L}{3}$

Q. Figure shows a composite system of two uniform rods of lengths as indicated. Then the coordinates of the centre of mass of the system of rods are

(2L​,32L​)

(4L​,32L​)

(6L​,32L​)

(6L​,3L​)

Centre of mass of the uniform rod will lie at its centre xcm​=m1​+m2​m1​x1​+m2​x2​​ xcm​=3mm(2L​)+2m(0)​,ycm​=3m2m(L)+m(0)​ xcm​=6L​,ycm​=32L​

$(\frac{L}{2}, \frac{2 L}{3})$

$(\frac{L}{4}, \frac{2 L}{3})$

$(\frac{L}{6}, \frac{2 L}{3})$

$(\frac{L}{6}, \frac{L}{3})$

Centre of mass of the uniform rod will lie at its centre
$x_{c m} = \frac{m _{1} x _{1} + m _{2} x _{2}}{m _{1} + m _{2}}$
$x_{c m} = \frac{m ( \frac{L}{2} ) + 2 m ( 0 )}{3 m}, y_{c m} = \frac{2 m ( L ) + m ( 0 )}{3 m}$
$x_{c m} = \frac{L}{6}, y_{c m} = \frac{2 L}{3}$