Work Energy and...

A stone of mass $$1 kg$$ tied to a light inextensible string of length $$L=\dfrac{10}{3}m$$ is whirling in a circular path of radius $$L$$ in a vertical plane. If the ratio of the maximum tension in the string to the minimum is $$4$$ and if $$g$$ is taken to be $$10 \ m/s^2$$, then speed of stone at the highest point of the circle is

A car is accelerated on a leveled road and attains a velocity 4 times of its initial velocity. In this process the potential energy of the car

An 800 g ball is pulled up a slope as shown in the diagram. Calculate the potential energy it gains.

A pendulum hangs from the ceiling of a jeep moving with a speed, $$v$$, along a circle of radius, $$R$$. Find the angle with the vertical made by the pendulum.

A particle of mass $$m_0$$, travelling at speed $$v_0$$, strikes a stationary particle of mass $$2m_0$$. As a result, the particle of mass $$m_0$$ is deflected through $$45^o$$ and has a final speed of $$\dfrac {v_0}{\sqrt 2}$$. Then the speed of the particle of mass $$2m_0$$ after this collision is

what is the work done by a force $$4N$$ in moving the body from d $$=$$ 1m to 4m?

A spring of natural length $$l$$ is compressed vertically downward against the floor so that its compressed length becomes $$\displaystyle\frac{l}{2}$$. On releasing, the spring attains it's natural length. If $$k$$ is the stiffness constant of the spring, then the work done by the spring on the floor is

A heavy ball moving with speed $$v$$ collides with a tiny ball. The collision is elastic, then immediately after the impact, the second ball will move with a speed approximately equal to-

A particle moves along the x-axis from $$x=0$$ to $$x=5$$ m under the influence of a force given by $$F=7-2x+3x^2$$. The work done in the process is

 A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector $$\overrightarrow{a}$$ is correctly shown in