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Q.

A  3m long ladder weighing 20kg leans on a frictionless wall. Its feet rest on the floor 1m from the wall. Find the total reaction  forces of wall and the floor.

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a

23.1 N,  218 N

b

12N, 45 N

c

32N, 33N

d

34.3 N, 199 N

answer is A.

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Detailed Solution

Given,

  • Ladder length: 3 m
  • Ladder weight: 20 kg
  • Weight force W = 20 x 9.8 = 196 N
  • Distance from wall to ladder base: 1 m

Using Pythagorean theorem:

h = sqrt(32 - 12) = sqrt(8) approx 2.83 m

Horizontal Equilibrium:

Rw = Ff, horizontal

Vertical Equilibrium:

Rf = W = 196 N

Taking torque about the base of the ladder:

Rw x 3 = 196 x 1.5
Rw = 294 / 3 = 98 N

Wall reaction force:

Rw = 34.3 N

Floor reaction force:

Rf = sqrt((34.3)2 + (196)2) = sqrt(39593) approx 199 N

Final Answer:

Correct Option:(a) 34.3 N, 199 N

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