A horizontal clothesline is tied between 2 poles, 12 meters apart. When a mass of 1 kilograms is tied to the middle of the clothesline, it sags a distance of 4 meters. What is the magnitude of the tension on the ends of the clothesline

The  tension on the clotheslines is  

Explanation:

The  diagram illustrating this  question is  shown on the first uploaded image

From the question we are told that  

    The distance between the two poles is  

     The mass tie to the middle of the clotheslines

     The length at which the clotheslines sags is  

Generally the weight due to gravity at the middle of the  clotheslines is mathematically represented as

let the angle which the tension on the  clotheslines makes with the horizontal be   which mathematically evaluated using the SOHCAHTOA as follows

=>    

=>    

   So the vertical component of this  tension is  mathematically represented a  

Now at equilibrium the  net horizontal force is  zero which implies that

=>      

substituting values

substituting values

a. is the answer because they are not shared

d is the correct answer