Question

Two parallel forces $\mathrm{P}$ and $3\mathrm{P}$ act on a rigid body at points A and B respectively. If the forces are interchanged in position, the resultant will be displaced through a distance of

• A. $\left(\frac{1}{2}\right)AB$
• B. $\left(\frac{1}{3}\right)AB$
• C. $\left(\frac{1}{4}\right)AB$
• D. $\left(\frac{3}{4}\right)AB$

Answer 1

The correct option is A

$\left(\frac{1}{2}\right)AB$

Step 1: Given data

Parallel force $\mathrm{P}$ act on a rigid body at points A

Parallel force $3\mathrm{P}$ acts on a rigid body at points B

Step 2: Formula used

We use the resultant force formula

Step 3: Calculation

In the first case, if the resultant acts on C, then the AC

$=\frac{\left[AB\right]}{\left[P+\hspace{0.17em}3P\right]}$

$=\frac{AB}{1P+3P}$

$=\frac{AB}{(1+3)P}$

$=\left(\frac{3}{4}\right)AB$

In the second case. if the resultant acts on AD

$=\left\{\frac{\left[AB\right]}{\left[3P+P\right]}\right\}$

$=\frac{AB}{3P+1P}$

$=\frac{AB}{(3+\hspace{0.17em}1)P}$

$=\left(\frac{1}{4}\right)AB$

Now,

$CD=AC-AD$

$CD=\left(\frac{3}{4}\right)AB-\left(\frac{1}{4}\right)AB$

$CD=\left(\frac{1}{2}\right)AB$

The resultant will be displaced through a distance of $\left(\frac{1}{2}\right)AB$.