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

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2

one "light year" is the distance that light travels, through vacuum, in one julian year.   that's 365.25 days, of 24 hours each.