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A uniform ladder of length 13 m and weighing 250 N is placed against a smooth vertical wall with its lower end 5 m from the wall. The coefficient of friction between the ladder and floor is 0.3. What is the frictional force acting on the ladder at the point of contact between the ladder and the floor?
- a)75 N
- b)52 N
- c)65 N
- d)16 N
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A uniform ladder of length 13 m and weighing 250 N is placed against ...
Since the ladder is placed against a smooth vertical wall, therefore there will be no friction at the point of contact between the ladder and the wall (point B).
ΣFx = 0 ⇒ Fr = R2
ΣFy = 0 ⇒ R1 = W = 250 N
ΣMB = 0 ⇒ R1 × AC – Fr × BC – 250 × OC = 0
BC = √(132 – 52) = 12 m
250 × 5 – Fr × 12 – 250 × 2.5 = 0
Fr = 52.1 N
Note: Maximum force of friction available at the point of contact between the ladder and the floor = μR1 = 0.3 × 250 = 75 N > Fr
Most Upvoted Answer
A uniform ladder of length 13 m and weighing 250 N is placed against ...
Solution:
Given:
Length of the ladder (l) = 13 m
Weight of the ladder (W) = 250 N
Distance of the lower end of the ladder from the wall (d) = 5 m
Coefficient of friction between the ladder and the floor (μ) = 0.3
To find: Frictional force acting on the ladder at the point of contact between the ladder and the floor.
Assumptions:
1. The ladder is in equilibrium and does not move.
2. The ladder is uniform and its weight acts at its center of gravity.
3. The ladder is smooth at its point of contact with the wall.
Analysis:
1. Free body diagram of the ladder:
The ladder is in equilibrium and hence the net force acting on it is zero. Therefore, the forces acting on the ladder must balance each other.
- Weight of the ladder (W) acts vertically downwards at its center of gravity (CG).
- The normal force (N) acts vertically upwards at the point of contact between the ladder and the floor.
- The frictional force (F) acts horizontally to the left at the point of contact between the ladder and the floor.
- The force due to the wall (Wd) acts vertically upwards at the point of contact between the ladder and the wall.
2. Equations of equilibrium:
Taking moments about the point of contact between the ladder and the floor, we get:
Wd = N × d
Taking moments about the center of gravity of the ladder, we get:
F × l/2 = W × l/2
Using the equation of equilibrium in the vertical direction, we get:
N + Wd = W
Substituting the value of Wd from the first equation, we get:
N = W - Wd = W - N × d/l
Solving these equations, we get:
N = W/(1 + d/l) = 250/(1 + 5/13) = 150 N
F = W × μ = 250 × 0.3 = 75 N
Therefore, the frictional force acting on the ladder at the point of contact between the ladder and the floor is 75 N.
Answer: Option (B)
Given:
Length of the ladder (l) = 13 m
Weight of the ladder (W) = 250 N
Distance of the lower end of the ladder from the wall (d) = 5 m
Coefficient of friction between the ladder and the floor (μ) = 0.3
To find: Frictional force acting on the ladder at the point of contact between the ladder and the floor.
Assumptions:
1. The ladder is in equilibrium and does not move.
2. The ladder is uniform and its weight acts at its center of gravity.
3. The ladder is smooth at its point of contact with the wall.
Analysis:
1. Free body diagram of the ladder:
The ladder is in equilibrium and hence the net force acting on it is zero. Therefore, the forces acting on the ladder must balance each other.
- Weight of the ladder (W) acts vertically downwards at its center of gravity (CG).
- The normal force (N) acts vertically upwards at the point of contact between the ladder and the floor.
- The frictional force (F) acts horizontally to the left at the point of contact between the ladder and the floor.
- The force due to the wall (Wd) acts vertically upwards at the point of contact between the ladder and the wall.
2. Equations of equilibrium:
Taking moments about the point of contact between the ladder and the floor, we get:
Wd = N × d
Taking moments about the center of gravity of the ladder, we get:
F × l/2 = W × l/2
Using the equation of equilibrium in the vertical direction, we get:
N + Wd = W
Substituting the value of Wd from the first equation, we get:
N = W - Wd = W - N × d/l
Solving these equations, we get:
N = W/(1 + d/l) = 250/(1 + 5/13) = 150 N
F = W × μ = 250 × 0.3 = 75 N
Therefore, the frictional force acting on the ladder at the point of contact between the ladder and the floor is 75 N.
Answer: Option (B)
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A uniform ladder of length 13 m and weighing 250 N is placed against a smooth vertical wall with its lower end 5 m from the wall. The coefficient of friction between the ladder and floor is 0.3. What is the frictional force acting on the ladder at the point of contact between the ladder and the floor?a)75 Nb)52 Nc)65 Nd)16 NCorrect answer is option 'B'. Can you explain this answer?
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A uniform ladder of length 13 m and weighing 250 N is placed against a smooth vertical wall with its lower end 5 m from the wall. The coefficient of friction between the ladder and floor is 0.3. What is the frictional force acting on the ladder at the point of contact between the ladder and the floor?a)75 Nb)52 Nc)65 Nd)16 NCorrect answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A uniform ladder of length 13 m and weighing 250 N is placed against a smooth vertical wall with its lower end 5 m from the wall. The coefficient of friction between the ladder and floor is 0.3. What is the frictional force acting on the ladder at the point of contact between the ladder and the floor?a)75 Nb)52 Nc)65 Nd)16 NCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform ladder of length 13 m and weighing 250 N is placed against a smooth vertical wall with its lower end 5 m from the wall. The coefficient of friction between the ladder and floor is 0.3. What is the frictional force acting on the ladder at the point of contact between the ladder and the floor?a)75 Nb)52 Nc)65 Nd)16 NCorrect answer is option 'B'. Can you explain this answer?.
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