$A$ 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 .................. $J$.

$A$ heavy stone is thrown with speed $v$ from a cliff of height $h$. How and in which direction should it be thrown so that the stone hits the ground with maximum speed?

$A$ ball is moving to and fro about the lowest point $A$ of a smooth hemispherical bowl. If it is able to rise up to a height of $20 \,cm$ on either side of $A$,its speed at $A$ must be .......... $m/s$ (Take $g = 10 \,m/s^2$,mass of the body = $5 \,g$).

As shown in the figure,a particle of mass $10 \ kg$ is placed at a point $A$. When the particle is slightly displaced to its right,it starts moving and reaches the point $B$. The speed of the particle at $B$ is $x \ m/s$. (Take $g = 10 \ m/s^2$). The value of $x$ to the nearest integer is:

$A$ uniform chain of mass $m$ and length $l$ is on a smooth horizontal table with $\left(\frac{1}{n}\right)^{\text{th}}$ part of its length hanging from one end of the table. The velocity of the chain,when it completely slips off the table is

State the importance of the work-energy theorem. Is the work-energy theorem a scalar or a vector?