First slide

Location of centre on mass for multiple point masses

Question

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

Easy

A

1m
B

2.5m
C

3.5m
D

2.125m

Solution

$\large {x_{cm}} = \frac{{M{x_1} + m{x_2}}}{{M + m}}$
m₁ = 20kg, x₁= 2.5m and m₂ = 60kg, x₂= 2m
$\large \therefore {x_c} = \frac{{{m_1}{x_1} + {m_2}{x_2}}}{{{m_1} + {m_2}}} = \frac{{20 \times 2.5 + 60 \times 2}}{{20 + 60}} = 2.125m$

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