The position vector of the centre of mass $\vec r\, cm$ of an asymmetric uniform bar of negligible area of cross-section as shown in figure is
$\vec r\,cm = \frac{{13}}{8}L\hat x + \frac{5}{8}L\hat y$
$\vec r\,cm = \frac{{5}}{8}L\hat x + \frac{13}{8}L\hat y$
$\vec r\,cm = \frac{{3}}{8}L\hat x + \frac{11}{8}L\hat y$
$\vec r\,cm = \frac{{11}}{8}L\hat x + \frac{3}{8}L\hat y$
Two point masses $m$ and $M$ are separated by a distance $L$. The distance of the centre of mass of the system from m is
Four particle of masses $m, 2m, 3m$ and $4m$ are arranged at the corners of a parallelogram with each side equal to $a$ and one of the angle between two adjacent sides is $60^o$. The parallelogram lies in the $x-y$ plane with mass m at the origin and $4m$ on the $x-$ axis. The centre of mass of the arrangement will be located at
If a force $10 \widehat i +15 \widehat j + 25 \widehat k$ acts on a system and gives an acceleration $2 \widehat i + 3 \widehat j - 5 \widehat k$ to the centre of mass of the system, the mass of the system is
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 circular plate of diameter ' $a$ ' is kept in contact with a square plate of side $a$ as shown. The density of the material and the thickness are same everywhere. The centre of mass of composite system will be ...........