#### Answer

The correct answer is (d) 180 N.

#### Work Step by Step

We can find the rate of deceleration of the head.
$a = \frac{v-v_0}{t} = \frac{0-4.0~m/s}{0.20~s}$
$a = -20~m/s^2$
The magnitude of acceleration is $20~m/s^2$, and this acceleration is directed upward.
We can find the mass of the dancer's head.
$m = (0.094)(65~kg) = 6.11~kg$
We can find the average force $F_N$ exerted on the head by the neck.
$\sum F = ma$
$F_N - mg = ma$
$F_N = ma+mg$
$F_N = (6.11~kg)(20~m/s^2)+(6.11~kg)(9.80~m/s^2)$
$F_N = 180~N$
The correct answer is (d) 180 N.