$A$ particle of mass $m$ is moving in a horizontal circle of radius $r$ under a centripetal force equal to $-K/r^2$,where $K$ is a constant. The total energy of the particle is

$A$ body starts moving unidirectionally under the influence of a source of constant power. Which one of the graphs correctly shows the variation of displacement $(s)$ with time $(t)$?

In the diagram shown,there is no friction at any contact surface. Initially,the spring has no deformation. What will be the maximum deformation in the spring? Consider all the strings to be sufficiently large. Consider the spring constant to be $K$.

An athlete throws a shotput of mass $25 \,kg$ with an initial speed of $4 \,ms^{-1}$ at an angle of $45^{\circ}$ with the horizontal from a height of $2 \,m$ above the ground. Assuming air resistance to be negligible,the kinetic energy of the shotput when it just touches the ground is . . . . . . $\left(g=10 \,ms^{-2}\right)$ (in $\,J$)

$A$ particle of mass $m$ moving horizontally with velocity $v_0$ strikes a smooth wedge of mass $M$,as shown in the figure. After the collision,the particle starts moving up the inclined face of the wedge and rises to a height $h$. The final velocity of the wedge $v_2$ is

$A$ curved surface is shown in the figure. The portion $BCD$ is free of friction. There are three spherical balls of identical radii and masses. Balls are released from rest one by one from $A$,which is at a slightly greater height than $C$.
With the surface $AB$,ball $1$ has large enough friction to cause rolling down without slipping; ball $2$ has a small friction and ball $3$ has a negligible friction.
$(a)$ For which balls is total mechanical energy conserved?
$(b)$ Which ball$(s)$ can reach $D$?
$(c)$ For balls which do not reach $D$,which of the balls can reach back $A$?