Friction in Curved Roads

Q. What should be the value of coefficient of static friction between the tyre and the road, when a car travelling at speed of $60km{h}^{-1}$ makes a level turn of radius $40\text{m}$?

1. $0.5$
2. $0.66$
3. $0.71$
4. $0.80$

Q. A car is moving on a circular level road of radius $300\text{m}$. If the coefficient of static friction is $0.3$, maximum safe speed (in $\text{km/h}$) of the car can be

[Take $g=10{\text{m/s}}^2$]

Q. A car of mass $2000kg$ is moving with a constant speed of $10m{s}^{-1}$ on a circular path of radius $20\text{m}$ on a level road. What must be the frictional force between the car and the road so that the car does not slip on the road ?

1. ${10}^3\text{N}$
2. ${10}^5\text{N}$
3. ${10}^2\text{N}$
4. ${10}^4\text{N}$

Q. A circular road course track has a radius of $500\text{m}$ and is banked to ${10}^{\circ }$. If the coefficient of friction between the road and tyre is $0.25$, compute (i) the maximum speed to avoid slipping (ii) optimum speed to avoid wear and tear of the tyres. [Take $\tan {10}^{\circ }=0.1763$]

1. $46.74\text{m/s}$, $29.39\text{m/s}$
2. $30\text{m/s}$, $24\text{m/s}$
3. $74.46\text{m/s}$, $23.39\text{m/s}$
4. $50\text{m/s}$, $44\text{m/s}$

Q.

A 1500-kg car moving on a flat, horizontal road negotiates a curve. If the radius of the curve is 20.0 m and the coefficient of static friction between the tires and dry pavement is 0.50, find the maximum speed the car can have so that it still makes the turn successfully.

1. 20 m/s

2. 30 m/s

3. 10 m/s

4. 40 m/s

Q. A motor car has a width $1.1\text{m}$ between wheels. Its centre of gravity is $0.62\text{m}$ above the ground and the coefficient of friction between the wheels and the road is $0.8$. What is the maximum possible speed, if the centre of gravity inscribes a circle of radius $15\text{m}$ ? (Road surface is horizontal)

1. $11.23\text{m/s}$
2. $10.84\text{m/s}$
3. $7.64\text{m/s}$
4. $6.28\text{m/s}$

Q. A coin place on a rotating turntable just slips of it is placed at distance of $4cm$ from the centre. If angular velocity of the turntable is doubled, it will just slip at a distance of

1. $1cm$
2. $2cm$
3. $4cm$
4. $8cm$

Q. What should be the maximum speed with which a car can be driven through a curve of radius $18m$ without skidding (where, $g=10m{s}^{-2}$, coefficient of static friction between the rubber tyres and the roadway is $0.2$)?

1. $36.0km{h}^{-1}$
2. $18.0km{h}^{-1}$
3. $14.4km{h}^{-1}$
4. $21.6km{h}^{-1}$

Q. A car is moving on a levelled circular road of radius of curvature $300\text{m}$. If the coefficient of static friction is $0.3$ and acceleration due to gravity is $10m{s}^{-2}$, then maximum allowable speed for the car will be (in $km{h}^{-1})$

1. $30$
2. $81$
3. $108$
4. $162$

Q.

A car is negotiating a curve of radius R = 20 m on a banked road with banking angle $\theta$ and coefficient of friction $\mu$. Take speed of car as v.

$\begin{array}{cccccc}& \text{Column 1}& & \text{Column 2}& & \text{Column 3}\\ \left(I\right)& v=10\sqrt{2}m/s& \left(i\right)& \mu =0.2& \left(p\right)& \theta ={30}^{\circ }\\ \left(II\right)& v=20m/s& \left(ii\right)& \mu =0.4& \left(Q\right)& \theta ={45}^{\circ }\\ \left(III\right)& v=50m/s& \left(iii\right)& \mu =0.6& \left(R\right)& \theta ={37}^{\circ }\\ \left(IV\right)& v=5m/s& \left(iv\right)& \mu =0.8& \left(S\right)& \theta ={60}^{\circ }\end{array}$

In which case will the friction be zero ?

1. $\left(I\right)\left(i\right)\left(Q\right)$

2. $\left(II\right)\left(ii\right)\left(R\right)$

3. $\left(I\right)\left(iii\right)\left(R\right)$

4. $\left(II\right)\left(iii\right)\left(R\right)$

Q.

One end of a massless spring of spring constant 100 N/m and natural length 0.5 m is fixed and the other end is connected to a particle of mass 0.5 kg lying on a frictionless horizontal table. The spring remains horizontal. If the table is made to rotate at an angular velocity of 2 rad/s, find the elongation of the spring(approximately).

1. 1 cm

2. 51 cm

3. 50 cm

4. None of these

Q. Which friction comes into play when we try to move an objiect ar rest

1. Rolling Friction
2. Fluid Friction
3. Static Friction
4. Sliding Friction

Q. A lift is going up with uniform velocity. When brakes are applied, it slows down. A person in that lift experiences:

1. more weight
2. less weight
3. normal weight
4. zero weight

Q.

A car has to move on a level turn of radius 90 m. If the coefficient of static friction between the tyre and the road is 1.0, find the maximum speed the car can take without skidding.

1. 20 m/s

2. 30 m/s

3. 10 m/s

4. 40 m/s

Q.

A car has to move on a level turn of radius 90 m. If the coefficient of static friction between the tyre and the road is 1.0, find the maximum speed the car can take without skidding.

1. 20 m/s

2. 30 m/s

3. 10 m/s

4. 40 m/s

Q. Before reaching the ground, the monkey grabs the rope to stop her falls. What do the bananas do?

1. Move up
2. Move down
3. Oscillate in SHM
4. Stop

Q. For the arrangement in figure, the tension in the string to prevent it from sliding down is:

1. 6 N
2. 6.4 N
3. 0.4 N
4. zero

Q. Assertion :Animate object can accelerate in the absence of external force. Reason: Newton's second law is not applicable on animate object.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
3. Assertion is correct but Reason is incorrect.
4. Both Assertion and Reason are incorrect.

Q. A car of mass $m$ is moving on a level circular track of radius, $R$. If ${\mu }_s$ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by

1. $\sqrt{Rg/{\mu }_s}$
2. $\sqrt{{\mu }_{s}Rg}$
3. $\sqrt{mRg/{\mu }_s}$
4. $\sqrt{{\mu }_{s}mRg}$

Q. Which of the following term is wrong about kinetic friction?

1. It is a contact force.
2. It is an electro-magnetic force.
3. It opposes relative velocity.
4. It decreases speed of the object.

Q. Mark the correct statment :

1. An electron and a proton when released from rest in a uniform electric field experience the same force and the same acceleration.
2. A solid conducting sphere holds more charge than a hollow conducting sphere of the same radius.
3. No work is done in taking a positive charge from one point to another inside a negatively charged metallic sphere.
4. Two equipotential surfaces may intersect.

Q. Two boys are riding their bicycles on the same concrete road. One has new tyres on his bicycle while the other has tyres that are old and used. Which of them is more likely to skid while moving through a patch of the road which has lubricating oil spilled over it?

Q. A body has a velocity of (2i + 3j) m/s. Which of the following vectors is along the direction of friction?

1. 2i + 3j
2. 2i – 3j
3. –2i + 3j
4. –2i – 3j

Q.

A 1500-kg car moving o a flat, horizontal road negotiates a curve as show in figure. If the radius of the curve is 20.0 m and the coefficient of static friction between the tires and dry pavement is 0.50, find the maximum speed the car can have and still make the turn successfully.

1. 20 m/s

2. 30 m/s

3. 10 m/s

4. 40 m/s

Q.

A car has to move on a level turn of radius 90 m. If the coefficient of static friction between the tyre and the road is 1.0, find the maximum speed the car can take without skidding.

1. 10 m/s

2. 20 m/s

3. 30 m/s

4. 40 m/s

Q. A car is moving on a circular road of curvature 300 m.If the coefficient of friction is 0.3 and acceleration due to gravity is $10m/s^2$, the maximum speed the car can have is:

1. 30 km/hr
2. 81 km/hr
3. 108 km/hr
4. 162 km/hr

Q. A car is moving on a levelled circular road of radius of curvature $300\text{m}$. If the coefficient of static friction is $0.3$ and acceleration due to gravity is $10m{s}^{-2}$, then maximum allowable speed for the car will be (in $km{h}^{-1})$

1. $30$
2. $81$
3. $108$
4. $162$

Q. A man is stranded in the middle of a perfectly smooth island of ice, where there is no friction between the ground and his feet. Under these circumstances,

1. he can reach the desired corner by throwing any object in the same direction
2. he has no chance of reaching any corner of the island
3. he can reach the desired corner by walking on the ground in that direction
4. he can reach the desired corner by throwing any object in the opposite direction

Q. A car of mass $m$ is moving on a level circular track of radius $R$. If ${\mu }_s$ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by

1. $\sqrt{{\mu }_{s}mRg}$
2. $\sqrt{{\mu }_{s}Rg}$
3. $\sqrt{mRg/{\mu }_s}$
4. $\sqrt{Rg/{\mu }_s}$

Q. Describe briefly how can you arrive at Archimedes' principle theoretically.