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A body of mass \( m=10^{-2} \mathrm{~kg} \) is moving in a medium and experience a frictional force \( F=-k v^{2} \). Its initial speed is \( v_{0}=10 \mathrm{~ms}^{-1} \). If, after \( 10 \mathrm{~s} \), its energy is \( \frac{1}{8} m v_{0}^{2} \), the value of \( k \) will be
(a) \( 10^{-4} \mathrm{~kg} \mathrm{~m}^{-1} \)
(b) \( 10^{-1} \mathrm{~kg} \mathrm{~m} \mathrm{~m}^{-1} \mathrm{~s}^{-1} \)
(c) \( 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1} \)
(d) \( 10^{-3} \mathrm{~kg} \mathrm{~s}^{-1} \)
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