Level Road & Rotating Platform

A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is 5 rad/s. The coefficient of friction between the drum’s inner wall surface and mass is _________. (Take $g = 10\text{ m/s}^2$)

On a dry curved (banked) road, with banking angle of zero, the maximum safe speed for a moving vehicle is '$v$'. After heavy rain, the maximum safe speed for the same road was reduced by 60%. The ratio of the coefficient of friction for the dry road to that of the wet road is

A large drum having radius $R$ is spinning around its axis with angular velocity $\omega$, as shown in figure. The minimum value of $\omega$ so that a body of mass $M$ remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass $M$ as $\mu$, is:

A motor cyclist has to rotate in horizontal circles inside the cylindrical wall of inner radius ' $R$ ' metre. If the coefficient of friction between the wall and the tyres is ' $\mu_s$ ', then the minimum speed required is ( $g =$ acceleration due to gravity)

A coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu$. If the distance of the coin from the center of the disc is $r$, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is:

On dry road, the maximum speed of a vehicle along a circular path is '$V$'. When the road becomes wet, maximum speed becomes $\frac{V}{2}$. If coefficient of friction of dry road is '$\mu$' then that of wet road is

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if the coefficient of friction between tyres and road is 0.34. [take g = 10 ms $^{-2}$]

A coin placed on a rotating table just slips when it is placed at a distance of $1\text{ cm}$ from the center. If the angular velocity of the table is halved, it will just slip when placed at a distance of _________ from the centre:

A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$. The beaker will revolve with the disc if:

A curve in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be 30 m/s without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ___________ m/s.

Statement I: A cyclist is moving on an unbanked road with a speed of 7 kmh${}^{-1}$ and takes a sharp circular turn along a path of radius of 2m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve. (g = 9.8 m/s2)

Statement II: If the road is banked at an angle of 45$^\circ$, cyclist can cross the curve of 2m radius with the speed of 18.5 kmh${}^{-1}$ without slipping.

In the light of the above statements, choose the correct answer from the options given below.

A modern grand - prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v. If the coefficient of static friction between the tyres and the track is $\mu$s, then the magnitude of negative lift FL acting downwards on the car is: (Assume forces on the four tyres are identical and g = acceleration due to gravity)

A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of $3.5$ revolutions per second. A coin placed at a distance of 1.25 cm from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is: (g = 10 m/s2)

Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute(rpm) to ensure proper mixing is close to:

(Take the radius of the drum to be 1.25 m and its axle to be horizontal):

The maximum velocity (in $\text{m s}^{-1}$) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction $0.6$ to avoid skidding is