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The roadway of a bridge over a canal is in the form of a circular arc of radius 18 m. What is the greatest speed with which a motorcycle can cross the bridge without leaving the ground ?
(a) $\sqrt{9.8}$ m/sec
(b) $\sqrt{18 \times 9.8}$ m/sec
(c) $18 \times 9.8$ m/sec
(d) $18/9.8$ m/sec

A car of mass \(m\) is moving on a level circular track of radius \(R\). If \(\mu_s\) represent the static friction between the road and tyres of the car, then the maximum speed of the car in circular motion is given by:

Two stones of masses \(m\) and \(2m\) are whirled in horizontal circles, the heavier one in a radius \(\frac{r}{2}\) and the lighter one in the radius \(r.\) The tangential speed of lighter stone is \(n\) times that of heavier stone when they experience the same centripetal forces. The value of \(n\) is:

A long horizontal rod has a bead which can slide along its length, and initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with constant angular acceleration $\alpha$. If the coefficient of friction between the rod and the bead is μ, and gravity is neglected, then the time after which the bead starts slipping is
(1) $\sqrt{\frac{\mu }{\alpha }}$
(2) $\frac{\mu }{\sqrt{\alpha }}$
(3) $\frac{1}{\sqrt{\mu \alpha }}$
(4) Infinitesimal

A car of mass \(1000\) kg negotiates a banked curve of radius \(90\) m on a frictionless road. If the banking angle is of \(45^\circ,\) the speed of the car is:

What is the minimum velocity with which a body of mass \(m\) must enter a vertical loop of radius \(R\) so that it can complete the loop?
1. \(\sqrt{2 g R}\)
2. \(\sqrt{3 g R}\)
3. \(\sqrt{5 g R}\)
4. \(\sqrt{ g R}\)$\mathrm{}$

At what point normal reaction will be maximum?
             
1.  A
2.  B
3.  C
4.  At both point A and B 

A string of length L is fixed at one end and carries a mass M at the other end. The string makes 2/π revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is 

(1) ML
(2) 2 ML
(3) 4 ML
(4) 16 ML