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Question
A ladder is resting with one end on a vertical wall and the other end on a horizontal floor. If it more likely to slip when a man stands near the bottom or near the top?
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Solution
The ladder is more likely to slide when the man stands near the top. This is because when the man stands near the top, it creates more torque compared to the torque caused by the weight of man near the bottom.
When the man stands near the bottom, the Centre of Gravity of the ladder is shifted to `C'` from `C` . Now, the couple due to forces (m + M)g and N makes the ladder fall . We see that due to its shift from `C` to `C',` the moment arm of the couple decreases from `r` to `r';` hence, the couple decreases.
When the man stands near the top of the ladder, the Centre of Mass shifts from `C` to `C'.` This increases the moment arm of the couple and from `r` to `r'.`
Increase in moment arm increases the couple and thus, the ladder easily falls.
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