Question

A body of mass 10 kg is resting on a rough horizontal surface of coefficient of friction 0.3. When 15 N force is applied horizontally on the body, then the friction force developed between the surface and the body will be: (Take g = 9.8 m/s²)
1. 29.4 N
2. 15 N
3. 3 N
4. 4.5 N

Answer 1

Correct Answer - Option 2 : 15 N

CONCEPT:

Friction:

• The resistance offered by the surfaces that are in contact with each other when they move over each other is called friction.
• Factors affecting friction:
  1. ​​Types of surfaces in contact.
  2. The normal force between the two surfaces.
• Friction force does not depend on the velocity of the object.
• The friction force developed in the static body will always be equal to the force applied to the body.
• The maximum/limiting friction force that can be developed in a static body is given as,

⇒ F_max = μN

Where F_max = limiting friction force, μ = coefficient of friction, and N = normal reaction

CALCULATION:

Given m = 10 kg, μ = 0.3, and (applied force) F = 15 N

• The normal reaction of the body is given as,

⇒ N = mg

⇒ N = 10 × 9.8

⇒ N = 98 N

• The limiting friction force is given as,

⇒ Fmax = μN

⇒ Fmax = 0.3 × 98

⇒ Fmax = 29.4 N

• Since the applied force is less than the limiting friction force, so the body will remain at rest after applying the force.
• The friction force developed in the static body will always be equal to the force applied to the body.
• So the developed friction force will be,

⇒ F_f = 15 N

• Hence, option 2 is correct.