Work Energy and...

The simple $$2 kg$$ pendulum is released from rest in the horizontal position. As it reaches the bottom position, the cord wraps around the smooth fixed pin at $$B$$ and continues in the smaller are in the vertical plane. Calculate the magnitude of the force $$R$$ supported by the pin at $$B$$ when the pendulum passes the position $$\displaystyle \theta = 30^{\circ}.\left ( g= 9.8m/s^{2} \right )$$

The bob of the pendulum shown in figure describes an arc of circle in a vertical plane. If the tension in the cord is $$2.5\ times$$ the weight of the bob for the position shown. Find the velocity and the acceleration of the bob in that position.

The mass of the bob of a simple pendulum of length $$L$$ is $$m$$. If the bob is left from its horizontal position then the speedof the bob and the tension in the thread in the lowest position of the bob will be respectively:

A weightless thread can withstand tension upto $$30\;N$$. A stone of mass $$0.5\ kg$$ is tied to it and is revolved in a circular path of radius $$2\ m$$ in a vertical plane. If $$g=10\ m/s^2$$, then the maximum angular velocity of the stone will be

A weightless thread can bear tension upto $$3.7\;kg$$ wt. A stone of mass $$500\;gm$$ is tied to it and revolved in a circular path of radius $$4m$$ in a vertical plane. If $$g=10\;ms^{-2}$$, then the maximum angular velocity of the stone will be:

A weightless thread can bear tension upto $$37 N$$. A stone of mass $$500 g$$ is tied to it and revolved in a circular path of radius $$4 m$$ in a vertical plane. If $$g=10 {ms}^{-2}$$, then the maximum angular velocity of the stone will be:

Stone tied at one end of light string is whirled round a vertical circle. If the difference between the maximum and minimum tension experienced by the string wire is $$2\ kg\ wt$$, then the mass of the stone must be

A spherical ball A of mass $$4\ kg$$, moving along a straight line strikes another spherical ball B of mass $$1\ kg$$ at rest. After the collision, A and B move with velocities $$v_{1}\ ms^{-1}$$ and $$v_{2}\ ms^{-1}$$ respectively making angles of $$30^{\circ}$$ and $$60^{\circ}$$ with respect to the original direction of motion of ball A. The ratio $$\dfrac {v_{1}}{v_{2}}$$ will be:

A body crosses the topmost point of a vertical circle with critical speed. What will be its centripetal acceleration when the string is horizontal. :-