Laws of Motion ...

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 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 $$\displaystyle \theta = 30^{\circ}.\left ( g= 9.8m/s^{2} \right )$$

A car is travelling along a circular curve that has a radius of $$50$$ m. If its speed is $$16$$ m/s and is incrcasing uniformly at $$\displaystyle 8m/s^{2}.$$ Determine the magnitude of its acceleration at this instant.

A uniform rod of length L is placed symmetrically on two walls as shown in the figure. The rod is in equilibrium. If $$N_1$$ and $$N_2$$ are the normal forces exerted by the walls on the rod then

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 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:

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 uniform rod of mass m and length L is suspended with two massless strings as shown in the figure. If the rod is at rest in a horizontal position the ratio of tension in the two strings $$T_1$$/$$T_2$$ is

Two uniform rods of equal length but different masses are rigidly joined to form an L-shaped body, which is then pivoted about O as shown in the figure. If the system is in equilibrium in the shown configuration. Then the ratio M/m will be: