When a body is acted upon by a resultant force,then the work done by the resultant force is equal to

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

$A$ ball of mass $300 g$ is dropped from a height $10 m$ above a sandy ground. On reaching the ground,it penetrates through a distance $1.5 m$ in sand and finally stops. The average resistance offered by the sand to oppose the motion is (acceleration due to gravity $= 10 m s^{-2}$) (in $N$)

Explain the conservation of mechanical energy using the example of a falling ball.

$A$ particle of mass $m$ is moving along a circle of radius $R$ such that its tangential acceleration $a_t$ varies with distance covered $x$ as $a_t = \alpha x^2$,where $\alpha$ is a constant. The kinetic energy $K$ of the particle varies with the distance as $K = \beta x^c$,where $\beta$ and $c$ are constants. The values of $\beta$ and $c$ are:

From a height of $h$ above the ground, a ball is projected up at an angle $30^{\circ}$ with the horizontal. If the ball strikes the ground with a speed of $1.25$ times its initial speed of $40 \,ms^{-1}$, the value of $h$ is (acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,m$)