Answer
(a) $k = 390~N/m$
(b) The spring will be 17.5 cm in length.
Work Step by Step
(a) The spring stretches by 5 cm. The force with which the spring pulls is equal to the object's weight. We can find the spring constant of the spring;
$kx = mg$
$k = \frac{mg}{x}$
$k = \frac{(2.0~kg)(9.80~m/s^2)}{0.05~m}$
$k = 390~N/m$
(b) We can find the amount that the spring stretches with a 3.0-kg object as;
$kx = mg$
$x = \frac{mg}{k}$
$x = \frac{(3.0~kg)(9.80~m/s^2)}{390~N/m}$
$x = 0.075~m = 7.5~cm$
Since the unstretched length of the spring is 10 cm, the spring will be 17.5 cm in length.
