Laws of Motion ...

A rubber ball of mass 50$$\mathrm { g }$$ falls from a height of $$\mathrm { m }$$ and rebounds to a height of .5$$\mathrm { m }$$ . The impulse between the ball and the ground if the time during which they are in contact was $$0,1$$ sec is

The minimum speed of a bucket full of water whirled in a vertical circle of radius  $$10 \ m$$  at the highest point so that the water may not fall  $$\left( g = 10 \mathrm { ms } ^ { - 2 } \right)$$

A car running with a velocity 72 kmph on a level road, is stopped after travelling a distance of 30 m after disengaging its engine $$\left( g={ 10ms }^{ -2 } \right) $$. The coefficient of friction between  the road and the tyres is.

A pendulum bob is held stationary by a horizontal force H. The three forces acting on the bob are shown in the diagram.
The tension in the string of the pendulum is T. The weight of the pendulum bob is W. The string is held at an angle of $$30^o$$ to the vertical.
Which statement is correct?

Impulse indicates.

The circumference of a circular track is $$400\pi/m$$. If the optimum speed with which a vehicle can be driven along it is to be $$20\ m/s$$, the angle of banking of the road must be about

As shown in figure, ball of of mass $$m \,kg$$  is suspended by a string $$\ell \,cm$$ long. Keeping the string always taut, the ball describes a horizontal circle of radius $$\dfrac{\ell}{2}$$. Calculate the angular speed.

If $$F = F_{0} (1 - e^{-t/\lambda})$$, the $$F-t$$ graph is

A road of width $$20$$m forms an arc of radius $$15$$ m, its outer edge is $$2$$m higher than its inner edge. For what velocity the road is banked?

A cyclist goes round a circular path of length $$400$$m in $$20$$ second. The angle through which he bends from vertical in order to maintain the balance is?