Laws of Motion ...

A stationary ball weighing $$0.25\  kg$$ acquires a speed of $$10 \ m/s$$ when hit by a hockey stick. The impulse imparted to the ball is:

Two ends of a uniform garland of mass $$m$$ and length $$L$$ are hanging vertically as shown. At instant $$t$$, the end Z is released. If $$y$$ is the distance moved by this end in time $$dt$$, change in momentum of an element of length $$dy$$ at a distance $$y$$ from Z is given as:

A pendulum was kept horizontal and released. Find the acceleration of the pendulum when it makes an angle $$ \theta $$ with the vertical.

What is the actual frictional force when the man has climbed $$1.0$$ m along the ladder?

A spool of mass $$M$$ and radius $$2R$$ lies on an inclined plane as shown in figure. A light thread is wound around the connecting tube of the spool and its free end carries a weight of mass $$m$$. The value of $$m$$ so that system is in equilibrium is

A particle P of mass m attached to vertical axis by two strings AP and BP of length l each. The separation AB=l. The point p rotates around the axis with an angular velocity $$\omega $$. the tension in two strings are $$ { T }_{ 1 }$$ and $$ { T }_{ 2 } $$
taut only if $$ \omega >\sqrt { \frac { 2g }{ l }  } $$

The spool shown in the figure is placed on a rough horizontal surface and has inner radius r and outer radius R. The angle $$\theta$$ between the applied force and the horizontal can be varied. The critical angle $$(\theta)$$ for which the spool does not roll and remains stationary is given by :

A particle of mass $$m$$ is suspended by a string of length $$l$$ from a fixed rigid support. A sufficient horizontal velocity $$\displaystyle v_{0}= \sqrt{3gl}$$ is imparted to it suddenly. Calculate the angle made by the string with the vertical when the acceleration of the particle is inclined to the string by $$\displaystyle 45^{\circ}.$$

A ball attached to one end of a string swings in a vertical plane such that its acceleration at point A (extreme position) is equal to its acceleration at point B (mean position). The angle $$\displaystyle \theta $$ is

just after it comes in contact with the peg.