The kinetic energy $K$ of a particle moving in a straight line depends upon the distance $s$ as $K = as^2$. The force acting on the particle is
$2\,as$
$2\,mas$
$2\,a$
$\sqrt {as^2}$
A frictionless track $ABCDE$ ends in a circular loop of radius $R$ .A body slides down the track from point $A$ which is at a height $h = 5\, cm$. Maximum value of $R$ for the body to successfully complete the loop is .................. $\mathrm{cm}$
A particle of mass $M$ is moving in a horizontal circle ofradius $R$ with uniform speed $v$. When it moves from one point to a diametrically opposite point, its
A force $F = - K(yi + xj)$ (where K is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point $(a, 0)$ and then parallel to the y-axis to the point $(a, a)$. The total work done by the force F on the particles is
A particle of mass $M$ starting from rest undergoes uniform acceleration. If the speed acquired in time $T$ is $V$, then power delivered to the particle in time $T$ is
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 .............. $\mathrm{mJ}$