Banking of Roads & Bridges

A car moving with a speed of $54\text{ km/h}$ takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take $g = 10\text{ m/s}^2$)

A car of mass m is crossing the convex bridge of radius of curvature R with speed V. At the highest point the thrust is ($g$ = gravitational acceleration)

A vehicle is moving with a constant speed of $10\text{ m/s}$ in a circular horizontal track of radius 20 m. A bob is suspended from the roof of a vehicle by a massless string. The angle made by the string with the vertical will be (acceleration due to gravity, $g = 10\text{ m/s}^2$)

Radius of curved road is ' $R$ ', width of road is ' $b$ '. The outer edge of road is raised by ' $h$ ' with respect to inner edge so that a car with velocity ' $V$ ' can pass safe over it, then value of ' $h$ ' is ( $g =$ acceleration due to gravity)

A vehicle is moving with uniform speed along 3 different shaped roads as horizontal, concave and convex. The surface of road on which, the normal reaction on vehicle is maximum is

A car is driven on the banked road of radius of curvature 20 m with maximum safe speed. In order to increase its safety speed by $20\%$, without changing the angle of banking, the increase in the radius of curvature will be [Assume friction is same on the road]

A car of mass ' $m$ ' moves on a banked road having radius ' $r$ ' and banking angle $\theta$. To avoid slipping from banked road, the maximum permissible speed of the car is $v_0$. The coefficient of friction $\mu$ between the wheels of the car and the banked road is

A train is moving with a speed of $12\text{ m/s}$ on rails which are $1.5\text{ m}$ apart. To negotiate a curve of radius $400\text{ m}$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $g = 10\text{ m/s}^2)$:

A car of $800\text{ kg}$ is taking turn on a banked road of radius $300\text{ m}$ and angle of banking $30^\circ$. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: $(g = 10\text{ m/s}^2, \sqrt{3} = 1.73)$

A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be: (Take g = 10 m/s$^{2}$)

A railway track is banked for a speed ',$v$' by elevating outer rail by a height '$h$' above the inner rail. The distance between two rails is 'd' then the radius of curvature of track is ( $g =$ gravitational acceleration)

The angle of banking '$\theta$' for a meter gauge railway line is given by $\theta = \tan^{-1}\left(\frac{1}{20}\right)$. What is the elevation of the outer rail above the inner rail?

The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a 30$^\circ$ banked road at maximum possible speed without skidding is ____________ $\times$ 103 kg m/s2. [Given cos30$^\circ$ = 0.87, $\mu$s = 0.2]