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:

A particle of mass m is suspended from a ceiling through a massless string. The particle moves in a horizontal circle as shown in the given figure. The tension in the string is:
 

1. mg

2. 2mg

3. 3mg

4. 4mg

A small coin is kept at a distance r from the centre of a gramophone disc rotating at an angular speed $\omega$. The minimum coefficient of friction for which a coin will not slip is:

1.  $\frac{{\mathrm{r\omega }}^2}{\mathrm{g}}$

2.  $\frac{\mathrm{g}}{{\mathrm{r\omega }}^2}$

3.  $\frac{{\mathrm{r}}^2{\mathrm{\omega }}^2}{\mathrm{g}}$

4.  $\frac{\mathrm{r\omega }}{\mathrm{g}}$

A ball of mass 0.1 Kg is whirled in a horizontal circle of radius 1 m by means of a string at an initial speed of 10 rpm. Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is:

A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between:

1.  14 m/s and 15 m/s

2.  15 m/s and 16 m/s

3.  16 m/s and 17 m/s

4.  13 m/s and 14 m/s

A body of mass m is moving on a concave bridge ABC of the radius of curvature R at a speed v. The normal reaction of the bridge on the body at the instant it is at the lowest point of the bridge is:

1.  $\mathrm{mg}$ $-$ $\frac{{\mathrm{mv}}^2}{\mathrm{R}}$

2.  $\mathrm{mg}$ $+$ $\frac{{\mathrm{mv}}^2}{\mathrm{R}}$

3.  mg

4.  $\frac{{\mathrm{mv}}^2}{\mathrm{R}}$

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: