A mass M = 4 kg attached to a string of length L = 2.0 m swings in a horizontal circle with a speed V. The string maintains a constant angle \theta\:=\:θ = 35.4 degrees with the vertical line through the pivot point as it swings. What is the speed V required to make this motion possible?

The velocity is  

Explanation:

The  diagram showing this set up is shown on the first uploaded image (reference Physics website )

From the question we are told that

    The mass is  m =  4 kg

    The  length of the string is

    The constant angle is  

Generally the vertical forces acting on the mass to keep it at equilibrium vertically is mathematically represented as

=>        

Now let the force acting on mass horizontally be k  so from SOHCAHTOA rule

=>      

Now this k is also equivalent to the centripetal force acting on the mass which is mathematically represented as

So

Which

=>      

So

=>      

=>      

Now the radius is evaluated using SOHCAHTOA rule as

=>    

substituting values

So

conservation of mass

mass before something happens = mass afterwards