Laws of Motion ...

The vertical section of a road over a canal bridge in the direction of its length is in the form of circle of radius $$8.9\;m$$. Then the greatest speed at which the car can cross this bridge without losing contact with the road at its highest point, the centre of gravity of the car being at a height $$h=1.1\;m$$ from the ground (Take $$g=10m/sec^2$$)

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

A metal bar $$70\ cm$$ long and $$4.00\ kg$$ in mass supported on two knife-edges placed $$10\ cm$$ from each end. A $$6.00\ kg$$ load is suspended at $$30\ cm$$ from one end. Find the reactions at the knife-edges. (Assume the bar to be of uniform cross section and homogeneous.)

An object is said to be in equilibrium when:
1. there is no net force acting on the object
2. the total clockwise moments about any point is equal to the total anti-clockwise moments about the same point
3. the object moves with constant velocity

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:

Assertion: A quick collision between two bodies is more violent than a slow collision; even when the initial and final velocities are identical.
Reason: The momentum is greater in first case

A massless meter stick is in equilibrium about its center point.
If a mass, $${m}_{1}=50 g$$, is placed at the $$30 cm$$ mark and a mass, $${m}_{2}=75 g$$, is placed at the $$70 cm$$ mark, where must a mass, $${m}_{3}=50 g$$, be placed to keep the system in equilibrium?

A car taken a turn along a curved road of radius $$40$$ m and the angle of banking of the road is $$\displaystyle {45} ^ {o} $$. At what maximum speed can the car be driven so that it may not skid. $$\displaystyle (g\ = {10\ ms} ^{-2} $$).

A small sphere is given vertical velocity of magnitude $$v_{0} = 5m/s$$ and it swings in a vertical plane about the end of massless string. The angle $$\theta$$ with the vertical at which string will break, knowing that it can withstand a maximum tension equal to twice the weight of the sphere, is $$[g = 10 m/s^{2}]$$.

A uniform meter sticks of mass 200 g is suspended from the ceiling through two verticle strings of equal lengths fixed at the ends. A small object of 20 g is placed on the stick at a distance of 70 cm from the left end. Find the tension in the two strings.