Question

Two forcess of 1.50 and 2N act vertically at the two ends of a metre scale. Where should a force be applied so that the scale remains stable. ​

Answer 1

Concept:

• As the metre scale will be under the force of earth(mg) , and also vertical forces applied from its Centre of mass will produce some torque.
• To remain the scale stable net torque should be balanced about Centre of mass.

Solution :

According to figure attached

• meter scale = length = 1m = 100cm

Translational equation:

$\implies\rm net \:force = 0$

$\implies\rm Force_{up}= Force_{down}$

$\implies\rm 1.5 + 2= F$

$\implies\rm F= 3.5\: N$

Rotational equation:

★ Clockwise torque = Anticlockwise torque (about centre of mass)

$\implies\rm \tau_{CW} = \tau_{ACW}$

$\implies\rm 1.5\times 50 + F(x) = 2\times 50$

$\implies\rm 75 + 3.5\times x= 100$

$\implies\rm 3.5\times x= 25$

$\implies\rm x= \dfrac{25}{3.5}$

$\implies\rm x = \dfrac{250}{35}$

$\implies\bf x= 7.14 cm$

★★so, force should be applied 7.14 cm from centre or 57.14 cm from one end of the metre scale.