$A$ block of mass $100\, g$ slides on a rough horizontal surface. If the speed of the block decreases from $10\, m/s$ to $5\, m/s,$ the thermal energy developed in the process is............. $J$.

The velocity at which the $6 \text{ kg}$ mass (shown in the figure) strikes the ground when it is released from a height of $6 \text{ m}$ above the ground is . . . . . . $\text{m/s}$. Assume the pulley is massless and the string is light and inextensible. (Take $g = 10 \text{ m/s}^2$)

$A$ small sphere of mass $m$ and radius $r$ slides down the smooth surface of a large hemispherical bowl of radius $R$. If the sphere starts sliding from rest, the total kinetic energy of the sphere at the lowest point $A$ of the bowl will be [given, moment of inertia of sphere $= \frac{2}{5} mr^2$].

$A$ uniform chain of length $3\, m$ and mass $3\, kg$ overhangs a smooth table with $2\, m$ laying on the table. If $k$ is the kinetic energy of the chain in joules as it completely slips off the table,then the value of $k$ is (Take $g = 10\, m/s^2$).

$A$ body is released from a height of $30 \ m$ vertically downwards. The speed of the body at which potential energy is twice that of kinetic energy is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)

$A$ block of mass $m$ is sliding down an inclined plane with constant speed. At a certain instant $t_0$,its height above the ground is $h$. The coefficient of kinetic friction between the block and the plane is $\mu$. If the block reaches the ground at a later instant $t_g$,then the energy dissipated by friction in the time interval $(t_g - t_0)$ is