The mass of a uniform ladder of length 5m is 20kg. A person of mass 60 kg stands on the ladder at a height of 2m from the bottom. The position of center of mass of the ladder and man from the bottom nearly is

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2.5 m

3.5 m

1 m

2.125 m

answer is D.

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Detailed Solution

length of the ladder = 5 m

Mass of the ladder = 20 kg

Mass of the person = 60 kg

$r_{1} = 2.5, r_{2} = 2$

$x_{cm} = \frac{m_{1} r_{1} + m_{2} r_{2}}{m_{1} + m_{2}}$

$= \frac{20 \times 2.5 + 60 \times 2}{20 + 60}$

$= \frac{50 + 120}{80} = \frac{170}{80} = \frac{17}{8} = 2.125 m$

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