Determine the length to three significant digits of each arc intercepted by a central angle $\theta$ in a circle of radius $r$. $r=15.1$ in., $\theta=210^{\circ}$

For the particle of Prob. $12.74$, determine the tangential component $F_t$ of the central force $\mathbf{F}$ along the tangent to the path of the particle for $(a) \theta=0$, (b) $\theta=45^{\circ}$.

A composite transposon integrated in a circular plasmid occasionally transposes the DNA comprising the original plasmid rather than the transposon’s central region. Explain how this is possible.

Design a double-slit apparatus so that the central diffraction peak contains precisely fifteen fringes. Assume the first diffraction minimum occurs at an interference maximum.

These exercise involve the formula for the area of a circular sector. The area of a sector of a circle with a central angle of $140^{\circ}$ is $70 \mathrm{m}^{2}.$ Find the radius of the circle.

The intensity of the central maximum in the interference pattern of a Young's double-slit experiment is about four times that of either light wave. Is this a violation of the law of conservation of energy?

Given a circular sector with radius L and central angle $\theta$, show that the area of the sector is given by

$$S=\frac{1}{2} L^2 \theta .$$

A box contains N identical gas molecules equally divided between its two halves. For N = 50, what is the percentage of the time the system spends in the central configuration?

A box contains N identical gas molecules equally divided between its two halves. Does the time spent in the central configuration increase or decrease with an increase in N?

The central nervous system is comprised of a. sympathetic and parasympathetic nervous systems b. organs and glands c. somatic and autonomic nervous systems d. brain and spinal cord

A box contains N identical gas molecules equally divided between its two halves. For N = 200, what is the percentage of the time the system spends in the central configuration?

Work each problem.

Find the radius of a circle in which a central angle of $\dfrac{\pi}{6}$ radian determines a sector of area $64 \mathrm{~m}^2$.

Find the area of each sector given its central angle $\theta$ and the radius of the circle. Round to the nearest tenth. $\theta=54^{\circ}, r=6$

What shape do you expect for a molecule with a central atom and the following pairings? Two bonding pairs of electrons and two non-bonding pairs of electrons