$A$ block of mass $1\,kg$ slides on a rough horizontal surface. If the speed of the block decreases from $10\,m/s$ to $8\,m/s$,the thermal energy developed in this process is .................. $J$.

$A$ uniform flexible chain of mass $m$ and length $2l$ hangs in equilibrium over a smooth horizontal pin of negligible diameter. What will be the speed of the chain when it leaves the pin?

What does the law of conservation of energy state?

An object of mass $8 \ kg$ moves under the influence of a force. The position of the object varies with time as $x = \frac{1}{2} t^2$,where $x$ is in meters and $t$ is in seconds. Find the work done by the force in the first $2 \ s$ in $J$.

$A$ lorry and a car moving with the same kinetic energy $(K.E.)$ are brought to rest by applying the same retarding force. Then:

The potential energy of a $1 \ kg$ particle free to move along the $x-$axis is given by: $U(x) = (\frac{x^4}{4} - \frac{x^2}{2}) \ J$. The total mechanical energy of the particle is $2 \ J$. Then,the maximum speed (in $m/s$) is: