17 January 2021 - Laws of Motion - Circular DynamicsContact Number: 9667591930 / 8527521718

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1.

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

2.

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, the maximum

speed of the car in circular motion is given by

(1) $\sqrt{{\mathrm{\mu}}_{\mathrm{s}}\mathrm{mRg}}$

(2) $\sqrt{\mathrm{Rg}/{\mathrm{\mu}}_{\mathrm{s}}}$

(3) $\sqrt{\mathrm{mRg}/{\mathrm{\mu}}_{\mathrm{s}}}$

(4) $\sqrt{{\mathrm{\mu}}_{\mathrm{s}}\mathrm{Rg}}$

3.

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 the value of heavier stone when they experience same centripetal forces. The value of n is

1. 2

2. 3

3. 4

4. 1

4.

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

5.

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45^{o}, the speed of the car is:

1. 20 ms^{-1}

2. 30 ms^{-2}

3. 5 ms^{-1}

4. 10 ms^{-1}

6.

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?

7.

At what point normal reaction will be maximum?

1. A

2. B

3. C

4. At both point A and B

8.

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*

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