In uniform circular motion, the factor that remains constant is.............

Answer:

The ratio is  [tex]k:d = 1 : 5[/tex]

Explanation:

From the question we are told that

   The first minimum of the single slit pattern falls on the fifth maximum of the double slit pattern.

Generally the condition for constructive interference for as single slit is  

     [tex]ksin(\theta) = n\lambda[/tex]

Here  k is the width of the slit  and n is the order of the fringe and for single slit n =  1 (cause we are considering the first maxima)

Generally the condition for constructive interference for as double slit is    

        [tex]dsin\theta = m\lambda[/tex]

Here  d is the separation between the  slit  and m is the order of the fringe and for double slit  m  =  5  (cause we are considering the first maxima)

=>     [tex]dsin\theta = 5\lambda[/tex]

So

       [tex]\frac{ksin(\theta)}{dsin(\theta)} = \frac{\lambda}{5\lambda}[/tex]

=>    [tex]\frac{k }{d} = \frac{1}{5}[/tex]

So  

      [tex]k:d = 1 : 5[/tex]

Answer:

Option C

Explanation:

Centripetal acceleration formula regarding velocity and radius is,

[tex]a_c=\frac{v^2}{r}[/tex]

now we know the centripetal acceleration is 9 and the radius is 16 so we plug these values into our formula,

[tex]a_c=\frac{v^2}{r}\\\\9=\frac{v^2}{16} \\\\144=v^2\\\\\sqrt{144}=v \\\\v=12\ m/s[/tex]

so velocity is 12 m/s

Now for the angular velocity, the formula of centripetal acceleration regarding angular velocity and radius is,

[tex]a_c=rw^2[/tex]

we know the centripetal acceleration is 9 and the radius is 16 so plug these values into the formula,

[tex]a_c=rw^2\\\\9=16w^2\\\\0.5625=w^2\\\\\sqrt{0.5625}=w \\\\0.75\ rad/s=w\\[/tex]

so angular velocity is 0.75 rad/s