The coordinates of the positions of particles of mass $7,\,4{\rm{ and 10}}\,gm$ are ${\rm{(1,}}\,{\rm{5,}}\, - {\rm{3),}}\,\,{\rm{(2,}}\,5,7{\rm{) }}$ and ${\rm{(3, 3, }} - {\rm{1)}}\,cm$ respectively. The position of the centre of mass of the system would be
$\left( { - \frac{{15}}{7},\frac{{85}}{{17}},\frac{1}{7}} \right){\rm{ }}cm$
$\left( {\frac{{15}}{7}, - \frac{{85}}{{17}},\frac{1}{7}} \right){\rm{ }}cm$
$\left( {\frac{{15}}{7},\frac{{85}}{{21}}, - \frac{1}{7}} \right){\rm{ }}cm$
$\left( {\frac{{15}}{7},\frac{{85}}{{21}},\frac{7}{3}} \right){\rm{ }}cm$
Define the position vector of centre of mass.
A piece of wood of mass $0.03\, kg$ is dropped from the top of a $100\, m$ height building. At the same time, a bullet of mass $0.02\, kg$ is fired vertically upward, with a velocity $100\, ms^{- 1}$, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is ........ $m$. $(g = 10\, ms^{-2})$
Two objects of mass $10\,kg$ and $20\,kg$ respectively are connected to the two ends of a rigid rod of length $10\,m$ with negligible mass. The distance of the center of mass of the system from the $10\,kg$ mass is :
Particles of masses $m, 2m, 3m,......nm$ $grams$ are placed on the same line at distances $l, 2l, 3l,....nl\, cm$ from a fixed point. The distance of centre of mass of the particles from the fixed point in centimetres is
Mass is distributed uniformly over a thin rectangular plate and positions of two vertices are given by $(1, 3)$ and $(2, -4)$. What is the position of $3^{rd}$ vertex if centre of mass of the plate lies at the origin ?