Answer:
k = 2.279
Explanation:
Given:
Magnitude of charge on each plate, Q = 172 μC
Now,
the capacitance, C of a capacitor is given as:
C = Q/V
where,
V is the potential difference
Thus, the capacitance due to the charge of 172 μC will be
C = 
Now, when the when the additional charge is accumulated
the capacitance (C') will be
C' = 
or
C' = 
now the dielectric constant (k) is given as:

substituting the values, we get

or
k = 2.279