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
When illuminated with monochromatic light, a double slit produces a pattern that is a combination of single-slit diffraction and double-slit interference. This can be easily seen if the separation between the slits and the size of slits are related by simple fractions. Find the ratio of the width of the slits to the separation between them, if the first minimum of the single slit pattern falls on the fifth maximum of the double slit pattern.
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]