A copper ball of mass $100 \mathrm{g}$ is at a temperature $T.$ It is dropped in a copper calorimeter of mass $100 \mathrm{g}$, filled with $170 \mathrm{g}$ of water at room temperature. Subsequently, the temperature of the system is found to be $75 °\mathrm{C}$. $T$ is (given, room temperature $=30 °\mathrm{C}$, specific heat of copper $=0.1 \mathrm{cal} {\mathrm{g}}^{-1} °{\mathrm{C}}^{-1}$)

A slender uniform rod of mass $M$ and length $l$ is pivoted at one end, so that it can rotate in a vertical plane (see the figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $\mathrm{\theta }$ with the vertical is,

Consider regular polygons with number of sides $n=3, 4, 5,\dots$ as shown in the figure. The centre of mass of all the polygons is at height $h$ from the ground. They roll on a horizontal surface about the leading vertex without slipping and sliding as depicted. The maximum increase in height of the locus of the centre of mass for each polygon is $\mathrm{\Delta }.$ Then, $\mathrm{\Delta }$ depends on $n$ and $h$ as,