A body of mass M is kept on a rough horizontal surface (friction coefficient = µ). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on A is F where
(a) F=Mg (b) F = µ Mg
(c) Mg ≤ F ≤ Mg√(1+µ2) (d) Mg ≥ F ≥ Mg√(1-µ2)
Answers
Weight of the body = mg.
Let the Horizontal Force be L.
∴ Resultant Force = √(L² + m²g²)
Now, we know that,
L ≤ friction (because body is not moving)
∴ L = friction = μmg (Maximum)
⇒ F ≤ √(μ²m²g² + m²g²)
∴ F ≤ mg√(μ²+ 1)
Now, This F will make angle θ with the Horizontal which will give FCosθ.
∴ F = mg - F Sinθ
∵ θ should always be less than 90° therefore, it can always be less than 1.
∴ F ≥ mg
∴ Mg ≤ F ≤ Mg√(1+µ2)
Hence, Option (c). is correct.
Hope it helps.
Answer:
Weight of the body = mg.
Let the Horizontal Force be L.
∴ Resultant Force = √(L² + m²g²)
Now, we know that,
L ≤ friction (because body is not moving)
∴ L = friction = μmg (Maximum)
⇒ F ≤ √(μ²m²g² + m²g²)
∴ F ≤ mg√(μ²+ 1)
Now, This F will make angle θ with the Horizontal which will give FCosθ.
∴ F = mg - F Sinθ
∵ θ should always be less than 90° therefore, it can always be less than 1.
∴ F ≥ mg
∴ Mg ≤ F ≤ Mg√(1+µ2)
Hence, Option (c). is correct.