Work Energy and...

Two wires $$AC$$ and $$BC$$ are tied at $$C$$ of a small sphere of mass $$5\ kg$$, which revolves at a constant speed $$v$$ in the horizontal plane with the speed $$v$$ of radius $$1.6\ m$$. Find the minimum value of $$v$$.

A force F is related to the position of a particle by the relation $$ F =(10x^2)N$$. The work done by the force when the particle moves from x=2m to x=4 m is

Which of the following is not an example of potential energy?

The velocity of a body moving in a vertical circle of radius r is $$\sqrt{7gr}$$ at the lowest point of the circle. What is the ratio of maximum and minimum tension?

A body of mass $$0.5\ kg$$ travels in a straight line with velocity $$v = ax^{3/2}$$ where $$a = 5\ m^{-1/2}s^{-1}$$. The work done by the net force during its displacement from $$x = 0$$ to $$x = 2m$$ is

A force $$F$$ acting on an object varies with distance $$x$$ as shown in the figure. The work done by the force in moving the object from $$x = 0$$ and $$x = 20\ m$$ is

A time-varying force $$F=6t-2{ t }^{ 2 } N$$, at $$t=0$$ starts acting on a body of mass $$2 kg$$ initially at rest, where t is in second. The force is withdrawn just at the instant when the body comes to rest again. We can see that at $$t=0$$,the force $$F=0$$. Now answer the following:
Mark the correct statement:

A man revolves a stone of mass m tied to the end of a string in a vertical circle of radius R, The net force at the lowest and height points of the circle directed vertical downwards are 
Here $$T_1, T_2$$ and  $$v_1, v_2$$ denote the tension in the string and the speed of the stone at the lowest and highest points, respectively.

A force $$F = -K(x\hat {i} + y\hat {j})$$ (where $$K$$ is a positive constant) acts on a particle moving in the $$x-y$$ plane. Starting from the origin, the particle is taken along the positive $$x-$$ axis to the point $$(a, 0)$$ and then to the point $$(a, a)$$. The total work done by the force $$\vec {F}$$ on the particle is

A spring of spring constant $$5\times {10}^{3}N/m$$ is stretched initially by $$5cm$$ from unstretched position. Then the work required to stretch is further by another $$5cm$$ is then