Answer
(a) $v = 3.93~m/s$
(b) The tension in the string is 6.2 N
Work Step by Step
(a) We can find the speed of the block.
$v = (75~rpm)(2\pi ~r)(\frac{1~min}{60~s})$
$v = (75~rpm)(2\pi)(0.50~m)(\frac{1~min}{60~s})$
$v = 3.93~m/s$
(b) The centripetal force is the net force which keeps an object moving in a circle. In this case, the tension provides the centripetal force.
$T = \frac{mv^2}{r}$
$T = \frac{(0.200~kg)(3.93~m/s)^2}{0.50~m}$
$T = 6.2~N$
The tension in the string is 6.2 N
