Banking of Roads

Q.

Assuming the coefficient of friction between the road and tyres of a car to be 0.5, the maximum speed with which the car can move round a curve of 40.0 m radius without slipping, if the road is unbanked, should be

1. 14m/s

2. 11m/s

3. 25 m/s

4. 19m/s

Q. {The velocity of a small ball of mass M and density d. when dropped in a container filled with glycerin is d}}_{2 }, the viscous force acting on the ball will be:

Q. a particle of mass m is moving on a circular path of radius r whith uniform speed v rate of change of linear momentum is propertional to 1 zero 2 independent of speed 3 propertional to v2 4 propertional to

Q. Two racing cars of masses m1 and m2 are moving in circles of radii r1 and r2 respectively. Their speeds are such that each makes a complete circle at the same time t. The ratio of the angular speeds of the first to the second car is 1) r1 :\:r2 2) m1 : m2 3) 1 : 1 4) m1m2 : r1r2

Q. 22.a particle of massm 2kg moves on circular path with const speed 10m/s .find change in speed and magnitude of change in velocity when particle completes half revolution .

Q. A particle of mass m tied to a string is moving in a vertical circular path such that the speed is just sufficient to complete the circle . String is light then find the acceleration of particle when it reaches at point A.

Q. A particle is moving on a circular track of radius 4 m such that its tangential acceleration is 2t m/$s^2$. If the particle starts from rest, then at what time the angle between velocity and acceleration will be ${45}^{\circ }$?

1. 5 sec
2. 4 sec
3. 3 sec
4. 2 sec

Q. A particle of mass m is being circulated on a vertical circle of radius r.If the speed of particle at heighest point be v the

Q. Three particles A (m=2kg) B (m=1kg) and C (m=1kg) are placed on the vertices P, Q, R respectively of an equilateral triangle PQR. Velocity of A is 1m/s along PQ, B is 1m/s along QR, and C is 1m/s along RP. What is velocity of the centre of mass?

Q. A plate is moving with velocity $5\text{m/s}$ parallel to a plate that is held stationary at a distance of $10\text{mm}$ below the upper plate. If the space between the plates is filled with water having coefficient of viscosity $9\times {10}^{-4}$ Pa $s$, then the shear stress acting on the surface of the moving plate assuming linear velocity profile between plates will be

1. $0.45{\text{Nm}}^{-2}$
2. $4.5\times {10}^{-3}{\text{Nm}}^{-2}$
3. $2\times {10}^{-4}{\text{Nm}}^{-2}$
4. ${10}^{-3}{\text{Nm}}^{-2}$

Q. A particle is constrained to move in a circle of radius $300\text{cm}$. Its linear speed increases with time as $v=2t$, where $t$ is in second and $v$ is in $\text{m/s}$. The acceleration of the particle at $t=3\text{s}$ is

1. $12{\text{m/s}}^2$
2. $2{\text{m/s}}^2$
3. $14{\text{m/s}}^2$
4. $12.16{\text{m/s}}^2$

Q. Q.A stone is tied in a string of length L and whirled in a vertical circle such that it just completes the circle. find the acceleration of the stone when the string is horizontal.

Q. a stone tied to one end of spring 80 cm long is whirled in horizontal circle with the cons†an t speed if stone makes 25 revolutions in 14 s then magnitude of acceleration of stone is?

Q. 75.the velocity of bullet reduces by 10 % in passing through a wooden plank . Find the number of such identical planks needed to stop the bullet

Q. Four particle of equal mass are moving round a circle of radius r due to their mutual gravitational attraction.Find the angular velocity of each particle?

Q. A thin circular ring of mass M and radius r​ is rotating about its axis with constant angular velocity omega. Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity?

Q. A circular road of radius $1000m$ has banking angle ${45}^o$. The maximum safe speed of a car having mass $2000kg$ will be, if coefficient of friction between tyre and road is $0.5$:

1. $172m/s$
2. $124m/s$
3. $99m/s$
4. $86m/s$

Q. A circular racket of radius 300 m is backed at an angle of ${15}^0$. The coefficient of friction between the wheels of a race car and the road is 0.2. the maximum permissible speed to avoid slipping is
( Take tan ${15}^0=0.27,g=10m{s}^{-2}$)

1. 18.6 $m{s}^{-1}$
2. 28.6 $m{s}^{-1}$
3. 48.6 $m{s}^{-1}$
4. 38.6 $m{s}^{-1}$

Q. A cubical block A of mass 10 kg and a block B of mass 2 kg are connected via string-pulley system as shown in the figure. If one end of the string is pulled with a force 20 N as shown, then the acceleration of wedge will be (All surfaces are smooth. Pulley and strings are ideal)

Q. 3.A disc of mass M kg and radius R metre is rotating at an angular speed of w rad/s when the motor is switched off. Neglecting the friction at the axle, the force that must be applied tangentially to the wheel to bring it to rest in time t is

Q. A motor cyclist at a speed of 5 m/s is describing a circle of radius 25 m. Find his inclination with vertical. What is the value of coefficient of friction between type and ground ?

Q. a particle of mass m moves with cons†an t speed v on a circular path of radius r.find magnitude of average foce on it in one fourth revolution

Q. A turn of radius $20$ m is banked for the vehicle going at speed of $36$ km/hr. If the coefficient of static friction between the road and the tyre is $0.4$. What of the following speeds are possible such that the vehicle neither slips down nor skids up ?

1. $20$ km/hr
2. $30$ km/hr
3. $40$ km/hr
4. $50$ km/hr

Q. A circular race-car track of radius $300\text{m}$ is banked at an angle of ${15}^{\circ }$. If the coefficient of static friction between the wheels of the race-car and the road is $0.2$, what is the maximum permissible speed to avoid slipping? Take $\tan {15}^{\circ }=0.27,g=10{\text{m/s}}^2$.

1. $48\text{m/s}$
2. $30\text{m/s}$
3. $17\text{m/s}$
4. $38.60\text{m/s}$

Q.

A road is banked such that a vehicle can go in the middle of it with a constant velocity of 40 m/s. What will happen if the velocity is decreased and why?
Imagine friction is not present

1. None of these

2. The vehicle will slide down as centripetal force mv²/R has to be constant

3. The vehicle will slide down as Normal by ground will decrease.

4. The vehicle slide up as Normal by ground will increase

Q. A 8000 kg engine pulls a train of five wagons each of 2000 kg along a horizontal track. If the engine exerts a force of 40000 N and the track offers a Friction force of 5000N, then calculate : a. The net accelerating force ; b. The acceleration of the train ; and c. The force of wagon 1 on wagon 2

Q. 8181J(4)(3)24In given figure, if acceleration of 2 kg and 3 kg area, respectively then relation between a18.and a2andisT2(1) a= 2a2(2) 2a, 3a23a, 2a2 TT(4) 2a, a2113 kgT2-24T 322 kg19. A particle of mass m is moving with constant speedv in a circular path of radius r. The power delivered

Q. Four particles of equal mass are moving in a circle of radius R due to their mutual gravitational attraction. Find the angular velocity of each particle

Q. 50 A horizontal force 10 N is necessary to just holda block stationary against a wall. The coefficient offriction between the block and the wall is 0.2, theweight of the block is(1) 20 N(2) 50 N(3) 100 N(4) 2 N

Q.

A curve has a radius of 50 meters and a banking angle of 15º. What is the ideal, or critical, speed (the speed for which no friction is required between the car's tires and the surface) for a car on this curve?

1. 7 m/s
2. 11 m/s
3. 14 m/s
4. 16 m/s