A ladder is at rest with its upper end against a wall and its lower end on the ground. A worker is about to climb it. When is it more likely to slip? (A) Before the worker is on it. (B) When the worker is on the lowest rung. (C) When the worker is halfway up the ladder. (D) When the worker is on the top rung.

Question

Deepak Patra · Answer

Assume that the ladder was initially in rotational equilibrium, when the worker was not on the ladder. Therefore the torque from the normal forces on ladder from the horizontal surface is equal to the torque from the vertical surface on ladder.
The torque from the weight of the worker is in the direction of the torque from the normal force on ladder, produced by the vertical surface. Therefore for the ladder to stay in rotational equilibrium, the torque on ladder from the normal force produced by the horizontal surface must increase.
This increase is possible when the worker is on the lower rung, but as the worker goes high, the magnitude of normal force from the vertical surface would increase, thereby increasing the risk of slipping of ladder.
Therefore (C) is the correct option while the rest are ruled out.

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