$A$ body dropped from height $H$ reaches the ground with a speed of $1.1 \sqrt{gH}$. Calculate the work done by air friction in terms of $mgH$.

Consider an elliptically shaped rail $PQ$ in the vertical plane with $OP = 3 \ m$ and $OQ = 4 \ m$. $A$ block of mass $1 \ kg$ is pulled along the rail from $P$ to $Q$ with a force of $18 \ N$,which is always parallel to the line $PQ$ (see the figure). Assuming no frictional losses,the kinetic energy of the block when it reaches $Q$ is $(n \times 10) \ J$. The value of $n$ is (take acceleration due to gravity $g = 10 \ m/s^2$):

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:

$A$ body of mass $1 \ kg$ is under a force, which causes a displacement given by $x = \frac{t^3}{3}$ (in $m$). Find the work done by the force in the first second (in $J$).

State and establish the principle of conservation of mechanical energy.

$A$ particle is placed at the point $A$ of a frictionless track $ABC$ as shown in the figure. It is gently pushed toward the right. The speed of the particle when it reaches the point $B$ is: (Take $g = 10 \ m/s^2$).