Laws of Motion ...

What is the value of $$p_1$$ and $$m_2$$ ?

A stone tied to a string of length $$L$$ is swired in a verticle circle with the other end of the string at the centre. At a certain instant of time the stone is at it lowest position and has a speed $$u$$. Find the magnitude of the change in its velocity as it reaches a position, where the string is horizontal.

A bob is suspended from a crane by a cable of length $$5m$$. The crane and load are moving at a constant speed $$v_{0}$$. The crane is stopped by a bumper and the bob on the cable swings out an angle of $$60^{\circ}$$. Find the initial speed $$v_{0}.(g=9.8 m/s^{2})$$

A simple pendulum is vibrating with angular amplitude of $$\theta=90^{o}$$ as shown in figure.
For what value of $$\theta$$ is the acceleration directed
$$(i)$$ Vertically upwards
$$(ii)$$ Horizontally
$$(iii)$$ Vertically downwards

A pendulum bob is raised to a height, $$h$$, and released from rest. At what height will it attain half of its maximum speed?

The kinetic energy of particle at the lower most position is

if AB is a massless string.

A simple pendulum of length $$l$$ has maximum angular displacement $$\displaystyle \theta .$$ Then maximum kinetic energy of a bob of mass $$m$$ is

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

Velocity of particle when it is moving vertically downward is