The position vector of the centre of mass r textcm of an asymmetric uniform bar of negligible area of cross-section as shown in figure is

Question

The position vector of the centre of mass r textcm of an asymmetric uniform bar of negligible area of cross-section as shown in figure is (A) r =(13/8) L hat x +(5/8) L hat y  (B) r =(11/8) L hat x +(3/8) L hat y  (C) r =(3/8) L hat x +(11/8) L hat y  (D) r =(5/8) L hat x +(13/8) L hat y

Tardigrade Admin · Accepted Answer

Coordinates of centre of mass (COM) are given by

X_{COM} = \frac{m _{1} x _{1} + m _{2} x _{2} + m _{3} x _{3}}{m _{1} + m _{2} + m _{3}}

Y_{COM} = \frac{m _{1} y _{1} + m _{2} y _{2} + m _{3} y _{3}}{m _{1} + m _{2} + m _{3}}

For given system of rods, masses and coordinates of centre of rods are as shown.

So,

X_{COM} = (\frac{2 m L + m 2 L + m \frac{5 L}{2}}{4 m}) = \frac{13}{8} L

and

Y_{COM} = \frac{2 m L + m \times \frac{L}{2} + m \times 0}{4 m} = \frac{5 L}{8}

So, position vector of COM is

r_{COM} = X_{COM} \overset{x}{^} + Y_{COM} \overset{y}{^}

= \frac{13}{8} L \overset{x}{^} + \frac{5}{8} L \overset{y}{^}

Q. The position vector of the centre of mass $r_{cm}$ of an asymmetric uniform bar of negligible area of cross-section as shown in figure is

$r = \frac{13}{8} L \overset{x}{^} + \frac{5}{8} L \overset{y}{^}$

$r = \frac{11}{8} L \overset{x}{^} + \frac{3}{8} L \overset{y}{^}$

$r = \frac{3}{8} L \overset{x}{^} + \frac{11}{8} L \overset{y}{^}$

$r = \frac{5}{8} L \overset{x}{^} + \frac{13}{8} L \overset{y}{^}$

Q. The position vector of the centre of mass rcm​ of an asymmetric uniform bar of negligible area of cross-section as shown in figure is

r=813​Lx^+85​Ly^​

r=811​Lx^+83​Ly^​

r=83​Lx^+811​Ly^​

r=85​Lx^+813​Ly^​

Q. The position vector of the centre of mass $r_{cm}$ of an asymmetric uniform bar of negligible area of cross-section as shown in figure is

$r = \frac{13}{8} L \overset{x}{^} + \frac{5}{8} L \overset{y}{^}$

$r = \frac{11}{8} L \overset{x}{^} + \frac{3}{8} L \overset{y}{^}$

$r = \frac{3}{8} L \overset{x}{^} + \frac{11}{8} L \overset{y}{^}$

$r = \frac{5}{8} L \overset{x}{^} + \frac{13}{8} L \overset{y}{^}$