Question

A meter scale has been suspended horizontally in its middle a load of 10N is placed at one end of it .at what distance 4N effort be placed to balance it

Answer 1

Given:

A meter scale has been suspended horizontally in its middle. A load of 10N is placed at one end of it.

To find:

Distance at which 4 N effort should be applied to balance it.

Diagram:

$\boxed{\setlength{\unitlength}{1cm}\begin{picture}(7,3)\put(2,1){\line(1,0){3}}\put(5,1){\vector(0,-1){1}}\put(2.5,1){\vector(0,-1){0.75}}\put(3.5,1){\circle*{0.2}}\put(5.25,0){10\:N}\put(2,0){4\:N}\put(3.5,1.25){C}\put(4,2){\vector(1,0){1}}\put(3.25,2){1\:m}\put(3,2){\vector(-1,0){1}}\end{picture}}$

Calculation:

So, let's assume that 10N is applid at one end , i.e. 0.5 m from centre of scale. And let 4N be applied 'l' distance from centre (C) of scale.

In order to achieve Rotational Equilibrium, the sum of torques must be zero.

$\therefore \: \sum( \tau) = 0$

$= > (10 \times 0.5) - (4 \times l) = 0$

$= > 5 - (4 \times l) = 0$

$= > 4l = 5$

$= > l = \dfrac{5}{4}$

$= > l = 1.25 \: m$

Since it is a metre scale , l = 1.25 m is not possible , hence 4N cannot balance the scale.