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

The maximum constant speed with which a car can move on a flat horizontal circular road with the radius of curvature 20 m and a coefficient of static friction 0.5 is: (g = 10 $\mathrm{m}/{\mathrm{s}}^2$)

A 10 kg block is kept on a horizontal turntable that rotates at an angular velocity of 2 rad/s. If the distance of the block from the center of the table is 0.5 m, the net force on the block is:

1. 40 N

2. 20 N

3. 10 N

4. Zero

A massless string of length 1 m fixed at one end carries a mass of 2 kg at the other end. The string makes $\frac{2}{\mathrm{\pi }}$ rev/s around the axis through the fixed end as shown in the figure. The tension on the string will be:
            

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

Two masses, M and m, are attached to a vertical axis by weightless threads of combined length l. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity ω. If the tensions in the threads are the same during motion, the distance of M from the axis is:

1. $\frac{Ml}{M+m}$

2. $\frac{ml}{M+m}$

3. $\frac{M+m}{M}l$

4. $\frac{M+m}{m}l$

A coin placed on a rotating table just slips if it is placed at a distance 4r from the center. On doubling the angular velocity of the table, the coin will just slip when the distance from the centre is equal to:-

1. 4r

2. 2r

3. r

4. $\frac{\mathrm{r}}{4}$