The centre of mass of a solid hemisphere of radius $8 \mathrm{cm}$ is $\mathrm{x} \mathrm{cm}$ from the centre of the flat surface. Then value of $\mathrm{x}$ is  

Three point particles of masses $1.0 \mathrm{k}\mathrm{g}, 1.5 \mathrm{kg}$ and $2.5 \mathrm{k}\mathrm{g}$ are placed at three corners of a right angle triangle of sides $4.0 \mathrm{c}\mathrm{m}, 3.0 \mathrm{c}\mathrm{m}$ and $5.0 \mathrm{c}\mathrm{m}$ as shown in the figure. The centre of mass of the system is at a point:

Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force $\mathrm{F}$ at a point $\mathrm{b}$ above its centre of mass (see figure). If the coefficient of friction is $\mu =0.4$ , the maximum possible value of $100\times \frac{\mathrm{b}}{\mathrm{a}}$ for a box not to topple before moving is ________