Mass is distributed uniformly over a thin square plate. If two end points of a diagonal are $(-2, 0)$ and $(2, 2)$,what are the coordinates of the centre of mass of the plate?

$A$ metre stick of mass $400 \ g$ is pivoted at one end and displaced through an angle $60^o$. The increase in its potential energy is ..... $J$.

Four identical particles each of mass $m$ are kept at the four corners of a square of side $a$. If one of the particles is removed,the shift in the position of the centre of mass is

The variation of density of a solid cylindrical rod of cross-sectional area $\alpha$ and length $L$ is given by $\rho = \rho_0 \frac{x^2}{L^2}$, where $x$ is the distance from one end of the rod. The position of its centre of mass from that end $(x=0)$ is:

Four particles of masses $m_1 = 2m$,$m_2 = 4m$,$m_3 = m$,and $m_4$ are placed at the four corners of a square. What should be the value of $m_4$ so that the centre of mass of all the four particles is exactly at the centre of the square?

The figure below shows a shampoo bottle in a perfect cylindrical shape. In a simple experiment,the stability of the bottle filled with different amounts of shampoo volume is observed. The bottle is tilted from one side and then released. Let the angle $\theta$ depict the critical angular displacement resulting in the bottle losing its stability and tipping over. Choose the graph that correctly depicts the fraction $f$ of shampoo filled ($f=1$ corresponds to completely filled) versus the tipping angle $\theta$.