Question

Two parallel forces 20 N and 30N act at the ends A and B of a rod 1.5m long.
The resultant of the force will act at the point:
A.) 90cm from A
B.) 75cm from B
C.) 20cm from B
D.) 85cm from A

Answer 1

Hint: If two forces are parallel in nature then resultant force must be the addition of two vector forces. Remember rod cannot be moved. Use the formula of torque. Force will be torque while the body is moving.

Complete step by step solution:
Diagram:
Before solving the question, understand what the question wants to convey.
Question says that we have a rod of 1.5m long whose ends are A and B. Forces acting are 20N and 30N on each end of the rod respectively.
Aim: find out the distance or a point at which the resultant of force will act.
Consider any point on rod at which resultant of force will act, suppose y m from A.
So the remaining distance will be (1.5-y) m from point B.

So we need to apply resultant force in the opposite direction to prevent the rod from moving
.

Resultant of force is given by,
Resultant force=20+30=50N.
Use formula of torque which is given by,
Torque=distance*force acting

$\begin{align}
  & 20y=30(1.5-y) \\
 & 20y=4.5-30y \\
 & 2y=4.5-3y \\
\end{align}$

Arrange terms containing variables on one side and constants on the other side.

4.5=5y
y = 0.9 m or 90 cm.

Note: before solving any type of question, first understand the question and analyse the data given in the question. Then make the picture in mind of what we want to calculate. This will give a clear idea about how to write a solution.