A 4 m long rod of negligible weight is supported at a point 125 cm from its one end and a load of 18 kgf is suspended at a point 60 cm from the support on the shorter arm.

(a) If a weight W is placed at a distance of 250 cm from the support on the longer arm to balance the rod, find W.

(b) If a weight 5 kgf is kept to balance the rod, find its position.

(c) To which class of lever does it belong?

(a) The principle of moments states that —

Moment of the load about the fulcrum = Moment of the effort about the fulcrum

Given,

Load = 18kgf and 18 kgf load is placed at 60 cm from the support.

Effort = W and W kgf weight is placed at 250 cm from the support.

Substituting the values in the formula we get,

$18 \times 60 = W \times 250 \\[0.5em] \Rightarrow W = \dfrac{18 \times 60}{250} \\[0.5em] \Rightarrow W = 4.32 \\[0.5em]$

∴ W = 4.32 kgf

(b) The principle of moments states that —

Moment of the load about the fulcrum = Moment of the effort about the fulcrum

Given,

Load = 18kgf and 18 kgf load is placed at 60 cm from the support.

W = 5 kgf and 5 kgf weight is placed at d cm from the support.

Substituting the values in the formula we get,

$18 \times 60 = 5\times d \\[0.5em] \Rightarrow d = \dfrac{18 \times 60}{5} \\[0.5em] \Rightarrow d = 216 cm \\[0.5em]$

∴ d = 216 cm

(c) It belongs to class I lever as fulcrum is in between the effort and the load.