A uniform square plate abcd has a mass of $1 \,kg$. If two point masses each of $20 \,g$ are placed at the corners $b$ and $c$ as shown, then the centre of mass shifts on the line
$OW$
$OX$
$OY$
$OZ$
The centre of gravity of a body on the earth coincides with its centre of mass for a small object whereas for an extended object it may not. What is the qualitative meaning of small and extended in this regard ? For which of the following two coincides ? A building, a pond, a lake, a mountain ?
Find the centre of mass of three particles at the vertices of an equilateral triangle. The masses of the particles are $100\; g , 150 \;g ,$ and $200\; g$ respectively. Each side of the equilateral triangle is $0.5\; m$ long.
A rod of length is $3 \;m$ and its mass acting per unit length is directly proportional to distance $x$ from one of its end then its centre of gravity from that end will be at
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 ........ $m$. $(g = 10\, ms^{-2})$