Advanced Friction MCQs: Numerical Problems and Solutions

Friction MCQ Test!

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Total Marks: 60, Obtained Marks: 0

1. Which of the following statements about friction is true?

A. Friction always opposes the motion of an object

B. Friction can sometimes aid the motion of an object

C. Friction is independent of the surface roughness

D. Friction depends only on the speed of the object

The correct answer is B. While friction generally opposes motion, it can sometimes help, like providing grip for walking or driving.

2. What is the cause of friction between two surfaces?

A. Gravitational force

B. Molecular adhesion

C. Electrostatic forces

D. Roughness of surfaces

The correct answer is D. Friction occurs due to microscopic irregularities present on the surfaces that interlock and resist motion.

3. A block is placed on a rough horizontal surface. The force required to just move the block is called the:

A. Kinetic friction

B. Static friction

C. Limiting friction

D. Rolling friction

The correct answer is C. Limiting friction is the maximum static friction that acts just before the object starts moving.

4. Which of the following is not a type of friction?

A. Rolling friction

B. Sliding friction

C. Fluid friction

D. Gravitational friction

The correct answer is D. Gravitational friction does not exist, while the other types of friction (rolling, sliding, and fluid) are real.

5. The coefficient of friction (μ) between two surfaces is defined as:

A. The ratio of the normal force to the frictional force

B. The product of the normal force and frictional force

C. The ratio of the frictional force to the normal force

D. The sum of the frictional force and normal force

The correct answer is C. The coefficient of friction (μ) is the ratio of the frictional force (F) to the normal reaction (N), i.e., μ = F/N.

6. Which factor does not affect the friction between two surfaces?

A. Normal force

B. Roughness of surfaces

C. Contact area

D. Type of material

The correct answer is C. For dry friction, the contact area between two surfaces does not significantly affect the frictional force.

7. A car is moving at a constant speed on a road. What kind of friction is acting between the tires and the road?

A. Static friction

B. Kinetic friction

C. Limiting friction

D. Rolling friction

The correct answer is A. When a car moves at constant speed without skidding, static friction acts between the tires and the road, providing grip.

8. A block of mass 5 kg is placed on a rough horizontal surface. The coefficient of static friction between the block and the surface is 0.4. What is the maximum horizontal force that can be applied to the block without moving it?

A. 10.5 N

B. 15.6 N

C. 19.6 N

D. 25.2 N

The correct answer is C. The maximum force is given by \( F_{\text{max}} = \mu_s \cdot N \), where \( N = mg \). Substituting values gives: \[ F_{\text{max}} = 0.4 \cdot (5 \, \text{kg}) \cdot (9.8 \, \text{m/s}^2) = 19.6 \, \text{N} \].

9. A block is sliding on a rough horizontal surface with an initial velocity of 10 m/s. The coefficient of kinetic friction between the block and the surface is 0.2. How far will the block travel before coming to rest?

A. 10 m

B. 15 m

C. 25.5 m

D. 30 m

The correct answer is C. Using the equation \( v^2 = u^2 + 2as \), with \( u = 10 \, \text{m/s} \) and \( a = -\mu_k \cdot g = -0.2 \cdot 9.8 \), solving gives: \[ 0 = (10)^2 + 2 \cdot (-0.2 \cdot 9.8) \cdot s \] Hence, \( s = 25.5 \, \text{m} \).

10. A car weighing 1500 kg is moving at 72 km/h. If the brakes are applied and the car skids to a stop, what is the minimum stopping distance? Assume the coefficient of kinetic friction between the tires and the road is 0.7.

A. 20 m

B. 25 m

C. 29.2 m

D. 35 m

The correct answer is C. Converting 72 km/h to 20 m/s, the deceleration is \( a = \mu_k \cdot g = 0.7 \cdot 9.8 = 6.86 \, \text{m/s}^2 \). Using \( v^2 = u^2 + 2as \), with \( v = 0 \) and \( u = 20 \, \text{m/s} \): \[ 0 = (20)^2 + 2 \cdot (-6.86) \cdot s \] Solving gives \( s = 29.2 \, \text{m} \).

11. A 10 kg crate is pulled across a horizontal surface with a coefficient of kinetic friction of 0.3. If a horizontal force of 50 N is applied, what is the acceleration of the crate?

A. 1.5 m/s²

B. 1.8 m/s²

C. 2.06 m/s²

D. 2.5 m/s²

The correct answer is C. Calculate the frictional force \( F_f = \mu_k \cdot N \), where \( N = mg \). The frictional force is: \[ F_f = 0.3 \cdot (10 \, \text{kg}) \cdot (9.8 \, \text{m/s}^2) = 29.4 \, \text{N} \] The net force is: \[ F_{\text{net}} = F_{\text{applied}} - F_f = 50 \, \text{N} - 29.4 \, \text{N} = 20.6 \, \text{N} \] Using \( F_{\text{net}} = ma \), the acceleration is: \[ a = \frac{F_{\text{net}}}{m} = \frac{20.6 \, \text{N}}{10 \, \text{kg}} = 2.06 \, \text{m/s}^2 \]

12. A car of mass 1000 kg is negotiating a curve of radius 50 m on a flat road. The coefficient of static friction between the tires and the road is 0.6. What is the maximum speed the car can have without skidding?

A. 15 m/s

B. 16 m/s

C. 17 m/s

D. 17.15 m/s

The correct answer is D. The maximum speed \( v \) is determined by: \[ F_f = \mu_s \cdot N \] \[ F_f = 0.6 \cdot (1000 \, \text{kg}) \cdot (9.8 \, \text{m/s}^2) = 5880 \, \text{N} \] The centripetal force required is: \[ F_{\text{centripetal}} = \frac{mv^2}{r} \] Setting \( F_f = F_{\text{centripetal}} \): \[ 5880 = \frac{1000 \cdot v^2}{50} \] Solving for \( v \): \[ v^2 = \frac{5880 \cdot 50}{1000} = 294 \] \[ v = \sqrt{294} \approx 17.15 \, \text{m/s} \]

13. A box with a mass of 12 kg is sliding down a frictionless incline at an angle of 40° with the horizontal. If the coefficient of kinetic friction between the box and the incline is 0.5, what is the acceleration of the box down the incline?

A. 1.5 m/s²

B. 2.0 m/s²

C. 2.5 m/s²

D. 2.55 m/s²

The correct answer is D. The net force and acceleration are calculated as follows: \[ F_f = \mu_k \cdot N \] \[ N = mg \cdot \cos(\theta) = 12 \cdot 9.8 \cdot \cos(40^\circ) \approx 90.2 \, \text{N} \] \[ F_f = 0.5 \cdot 90.2 \approx 45.1 \, \text{N} \] \[ F_{\text{gravity, parallel}} = mg \cdot \sin(\theta) \approx 75.7 \, \text{N} \] \[ F_{\text{net}} = F_{\text{gravity, parallel}} - F_f = 75.7 - 45.1 = 30.6 \, \text{N} \] The acceleration is: \[ a = \frac{F_{\text{net}}}{m} = \frac{30.6 \, \text{N}}{12 \, \text{kg}} \approx 2.55 \, \text{m/s}^2 \]

14. A car of mass 1000 kg is negotiating a curve of radius 50 m on a flat road. The coefficient of static friction between the tires and the road is 0.6. What is the maximum speed the car can have without skidding?

A. 15 m/s

B. 16 m/s

C. 17 m/s

D. 17.15 m/s

The correct answer is D. The maximum speed \( v \) is determined by: \[ F_f = \mu_s \cdot N \] For a flat road, \( N = mg \), so: \[ F_f = 0.6 \cdot (1000 \, \text{kg}) \cdot (9.8 \, \text{m/s}^2) = 5880 \, \text{N} \] The centripetal force required is: \[ F_{\text{centripetal}} = \frac{mv^2}{r} \] Setting \( F_f = F_{\text{centripetal}} \): \[ 5880 = \frac{1000 \cdot v^2}{50} \] Solving for \( v \): \[ v^2 = \frac{5880 \cdot 50}{1000} = 294 \] \[ v = \sqrt{294} \approx 17.15 \, \text{m/s} \]

15. A block of mass 8 kg is placed on a frictionless incline of 30° to the horizontal. A horizontal force \( F \) is applied to the block, causing it to slide up the incline. If the coefficient of kinetic friction between the block and the incline is 0.4, what is the horizontal force required to make the block slide up the incline with an acceleration of 2 m/s²?

A. 70 N

B. 80 N

C. 85 N

D. 89.36 N

The correct answer is D. The horizontal force \( F \) is calculated as follows: \[ N = mg \cdot \cos(\theta) = 8 \cdot 9.8 \cdot \cos(30^\circ) \approx 85.4 \, \text{N} \] \[ F_f = \mu_k \cdot N = 0.4 \cdot 85.4 \approx 34.16 \, \text{N} \] \[ F_{\text{gravity, parallel}} = mg \cdot \sin(\theta) = 8 \cdot 9.8 \cdot \sin(30^\circ) \approx 39.2 \, \text{N} \] \[ F_{\text{net}} = m \cdot a = 8 \cdot 2 = 16 \, \text{N} \] \[ F = F_{\text{net}} + F_f + F_{\text{gravity, parallel}} = 16 + 34.16 + 39.2 \approx 89.36 \, \text{N} \]