A body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ metre. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is .............. $\mathrm{m} / \mathrm{s}$
$4.43$
$2$
$0.5 $
$19.6$
A force acts on a $3\, gm$ particle in such a way that the position of the particle as a function of time is given by $x = 3t -4t^2 + t^3$ , where $x$ is in $meters$ and $t$ is in $seconds$ . The work done during the first $4\, second$ is ................. $\mathrm{mJ}$
The length of a spring is $\alpha $ when a force of $4\,N$ is applied on it and the length is $\beta $ when $5\,N$ force is applied. Then the length of spring when $9\,N$ force is applied is
A vertical spring with force constant $K$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is
Which one of the following statement does not hold good when two balls of masses ${m_1}$ and ${m_2}$ undergo elastic collision
Power applied to a particle varies with time as $P = (4t^3 -5t + 2)\,watt$, where $t$ is in second. Find the change is its $K.E.$ between time $t = 2$ and $t = 4 \,sec.$ ............... $\mathrm{J}$