Question

The line of action of the resultant of two like parallel forces shifts by one-fourth of the distance between the forces when the two forces are interchanged.The ratio of two forces is?​

Answer 1

Answer:

the ratio of two force is x:x\4

Answer 2

Given that,

The resultant of two like parallel forces shifts by one-fourth of the distance between the forces.

We need to calculate the net force

Using formula of resultant

$F=F_{1}+F_{2}$

The torque about individual force and about net force should be equal.

We need to calculate the torque about F₁ and F

Using formula of torque

$(F_{1}+F_{2})\times x_{1}=F_{1}L$

$x_{1}=\dfrac{F_{1}L}{(F_{1}+F_{2})}......(I)$

When the two forces are interchanged

Then, the torque about F₂ and F is

$(F_{1}+F_{2})\times x_{2}=F_{2}L$

$x_{2}=\dfrac{F_{2}L}{(F_{1}+F_{2})}....(II)$

We need to calculate the ratio of two forces

On subtracting equation (II) from equation (I)

$x_{2}-x_{1}=\dfrac{L}{4}$

Put the value of x₁ and x₂

$\dfrac{F_{2}L}{F_{1}+F_{2}}-\dfrac{F_{1}L}{F_{1}+F_{2}}=\dfrac{L}{4}$

$\dfrac{F_{2}L-F_{1}L}{F_{1}+F_{2}}=\dfrac{L}{4}$

$4LF_{2}-4LF_{1}=F_{1}L+F_{2}L$

$3LF_{2}=5LF_{1}$

$\dfrac{F_{1}}{F_{2}}=\dfrac{3}{5}$

Hence, The ratio of two forces is 3:5.