Please be patient as the PDF generation may take upto a minute.

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 ${\mathrm{\mu }}_{\mathrm{s}}$ 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