$A$ particle is released from a height $s$. At a certain height,its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively:

$A$ closed circular tube of average radius $15\,cm$,whose inner walls are rough,is kept in a vertical plane. $A$ block of mass $1\,kg$ just fits inside the tube. The speed of the block is $22\,m/s$ when it is introduced at the top of the tube. After completing five oscillations,the block stops at the bottom region of the tube. The work done by the tube on the block is $......J$. [Given $g=10\,m/s^2$]

$A$ bob of a pendulum of length $0.5 \ m$ has a speed of $6 \ ms^{-1}$ at its lowest point. Find the speed of the bob when the string of the pendulum makes $60^{\circ}$ with the vertical. (Take $g=10 \ ms^{-2}$)

$A$ body of mass $0.5\, kg$ travels on a straight-line path with velocity $v = (3x^2 + 4)\, m/s$. The net work done by the force during its displacement from $x = 0$ to $x = 2\, m$ is $.......J$.

$A$ stone with weight $w$ is thrown vertically upward into the air from ground level with initial speed $v_0$. If a constant force $f$ due to air drag acts on the stone throughout its flight,the maximum height attained by the stone is

Under the action of a force,a $2 \, kg$ body moves such that its position $x$ as a function of time $t$ is given by $x = \frac{t^2}{3}$,where $x$ is in metres and $t$ is in seconds. The work done by the force in the first two seconds is .......... $J$.