# MHT-CET Physics Crash Course “Vehicle on Banked Road” Class 12

## “Vehicle on Banked Road” MHT-CET Class 12 Physics Crash Course| Chapter Rotational Dynamics

In this session G.S. Khairnar will discuss the theory and MCQ’s of “Vehicle on Banked Road”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.

### Velocity of vehicle on curved banked road:-

Hello dear students we know that the maximum safety speed for the vehicle moving along the curved horizontal road is given as,

The surface of road and so the frictional forces are changes due to some factors like rainfall, seasons etc. Hence force of friction is not reliable. Its magnitude decreases when the road becomes wet due to rains or when oil falls on the road.

Thus force of friction will not be able to produce necessary centripetal force and vehicle will skid off. To avoid this roads should be banked.

The elevation of outer edge of road over its inner edge is known as banking of road.

The angle between elevated surface of road and the horizontal surface of road is known as angle of banking.

Let’s find the velocity of a car on a banked road ……!

Consider a vehicle of mass ‘m’ moving velocity V along a curved banked road at an angle θ as shown in fig. below.

The force acting on vehicle is weight ‘mg’ acting vertically downward & normal reaction N.

The normal reaction ‘N’ can be resolved into two components.

1. Ncosθ- vertical component of N
2. Nsinθ – horizontal component of N

There is also frictional force bent tyros of vehicle & road surface which is resolved into two components.

1. f cosθ – along vertical direction
2. f sinθ – along horizontal direction

The component of normal reaction Ncosθ is balanced by weight ‘mg’ of vehicle & component f sinθ of frictional force.

∴ N cos θ = f sin θ + mg
∴ mg = N cos θ – f sin θ ………………… (1)

The component of normal reaction Nsinθ and frictional force fcosθ provides necessary centripetal force.

The above equation shows that the angle of banking is independent on mass of vehicle.

Equation (4) gives the maximum safety speed of vehicle moving along the curved banked road.

Equation (5) give s optimum speed of vehicle moving along curved banked road

Ex. Railway track of curvature 2 km has inclination of θ0 for a maximum velocity of 72 kmph. Find the value of θ.

Solution: Here, R= 2 km=2000 m

### Let’s solve the following MCQs……

Q.1) The maximum safety speed of vehicle moving along curved banked road is independent of …

a) mass of vehicle

b) friction

c) atmospheric conditions

a) mass of vehicle

Q.2) Suppose that the car of mass taking turn on curved banked road at certain speed, the direction of frictional force acting between surface of road and tyres of vehicle for the minimum speed is..…

a) along road and towards the centre of curvature

c) along road and away from centre of curvature

d) can not be predicted

c) along road and away from centre of curvature

Q.3) Suppose that the car of mass taking turn on curved banked road at certain speed, the direction of frictional force acting between surface of road and tyres of vehicle for the maximum speed is..…

a) along road and towards the centre of curvature

c) along road and away from centre of curvature

d) can not be predicted

a) along road and towards the centre of curvature

Q.4) Maximum safety speed of vehicle moving along curved banked road is ..…

Q.5) Minimum safety speed of vehicle moving along curved banked road is ..…

Q.6) Car of mass 2500 kg moving along a curved banked road of curvature 1 km. The angle of banking for which the most safe speed for car is 25 m/s. (Use g= 10 m/s2)

Q.7) Rail way track of curvature 2 km separated by 1 m. The elevation required for rail tracks so that train should run safely at speed of 72 kmph is

a) 4 mm

b) 4 cm

c) 4 m

d) 40 cm

Q.8) When a car takes a circular turn on a banked road, the Centripetal force is provided by…..

a) gravitational force

b) frictional force

c) horizontal component of normal reaction

d) vertical component of normal reaction.

c) If horizontal component of normal reaction

### ♦जिल्हा नुसार जाहिराती ♦

अहमदनगर अकोला अमरावती औरंगाबाद भंडारा बुलढाणा
चंद्रपुर धुले गढ़चिरौली गोंदिया हिंगोली जलगांव
जालना कोल्हापुर लातूर मुंबई नागपुर नांदेड़
नंदुरबार नाशिक उस्मानाबाद पालघर परभानी पुणे
रायगढ़ रत्नागिरि सांगली सातारा सिंधुदुर्ग सोलापुर
ठाणे वर्धा वाशिम यवतमाल बीड

### ♦शिक्षणानुसार जाहिराती ♦

७ वी (7th) दहावी (SSC) बारावी (HSC) डिप्लोमा आय.टी.आय पदवी
पदव्युत्तर शिक्षण बी.एड एम.एड एल.एल.बी / एल.एल.एम बीएससी एमबीए
बीसीए एमसीए बी.कॉम एम.कॉम GNM/ANM एमएससी
बी.फार्म एम.फार्म बी.ई एम.ई BAMS/BHMS एम.बी.बी.एस / एम.डी
बी.टेक एम.टेक MS-CIT