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 the center of mass of the ladder and man from the bottom is nearly

Answer 1

Explanation:

Ycm=

80

60×2+20×2.5

=2.1m

Answer 2

The mass of a uniform ladder of 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.

To find : The position of the center of mass of the ladder and man from the bottom is nearly.

solution : centre of mass of ladder must be the middle point of its length.

so position of centre of mass of ladder = (0, 5/2) = (0, 2.5 ) , it means mass of ladder is located at (0, 2.5).

a/c to question, man of mass 60 kg stands on the ladder at a height of 2m from the bottom.

so, position of man = (0, 2)

now position of C.O.M = [0, (m₁y₁ + m₂y₂)/(m₁ + m₂)]

= [0, (60 kg × 2m + 20 kg × 2.5m)/(60kg + 20kg)]

= [0, (120 + 50)/80]

= (0, 2.125)

Therefore the position of centre of mass of the ladder and the man from the bottom is nearly 2.1 m.