A force \( F \) is applied on a uniform horizontal rod of mass m kept on horizontal rough surface as shown. Cocfficient of friction varies is \( \mu_{0} x \), where \( x \) is distance from end \( A \) of the rod.
What is the minimum value of force so that rod starts moving ? (Rod does not topple)
(A) \( \frac{\mu_{0 mg } \ell}{\sqrt{1+\mu_{0}^{2} \ell^{2}}} \)
(B) \( \frac{ mg }{\sqrt{1+\mu_{0}^{2} \ell^{2}}} \)
(C) \( \frac{\mu_{0} mg \ell}{2 \sqrt{1+\mu_{0}^{2} \ell^{2}}} \)
(D) \( \frac{m g}{4} \)
