Question

A string 2 m long is tied to the ends of a uniform rod that weighs 60 n and 1.6 m long.the string passes over a nail that the rod hangs horizontally .what is the tension in the string?

Answer 1

Given :

Weight of the uniform rod :

= 60 N

Length of the rod :

= 1.6 m

Length of the string that is tied to the ends of the rod and passes over the nail is  :

= 2 m

To Find :

Tension in the string = ?

Solution :

We know that the force acting on the rod is its weight which is acting in downward direction and its magnitude is :

= 60 N

Let  us assume the angle between the string and the rod be :

= $\theta$

So , it will be given as :

$cos \theta = \frac{0.8}{1}$

      $= \frac{4}{5}$

So , $\theta = cos^{-1}(\frac{4}{5})$

And therefore  , $sin\theta = (\frac{3}{5})$

So , now using equilibrium condition we can write :

$mg = 2Tsin\theta$

where T is tension in string .

So , $T= \frac{mg}{2sin\theta}$

          $= \frac{60N}{2\times \frac{3}{5}}$

           = 50 N

So , the tension in the string T is 50 N.