A road is $10\,\, m$  wide. Its radius of curvature is $50\,\,m$ . The outer edge is above the lower edge by a distance of  $1.5\,\,m$ . this road is most suited for the velocity   ......... $m/\sec$

Objects $A$ and $B$ each of mass $m$ are connected by light inextensible cord. They are constrained to move on a frictionless ring in a vertical plane as shown in figure. The objects are released from rest at the positions shown. The tension in the cord just after release will be

A body of mass $8\,kg$ is hanging another body of mass $12\,kg$. The combination is being pulled by a string $T _2$ will be respectively: (use $g =9.8\,m / s ^2$ )

A child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u$ , the centre of mass of the system (trolley + child) will move with a speed

In the figure the tension in the diagonal string is $60\,N$.Find the magnitude of the horizontal force $\overline{ F }_1$ and $\overline{ F }_2$ that must be applied to hold the system in the position shown.what is the weight of the suspended block?

A block of mass $m$, is kept on a wedge of mass $M$, as shown in figure such that mass $m$ remains stationary w.r.t. wedge. The magnitude of force $P$ is