d
\(\begin{array}{l} Work\,done\,by\,tension\, + Work\,done\,by\,\\ force\left( {applied} \right) + Work\,done\,by\,gravitational\\ force = change\,in\,kinetic\,energy\\ Work\,done\,by\,tension\,is\,zero\\  \Rightarrow \,0 + F \times AB - Mg \times AC = 0\\  \Rightarrow F = Mg\left( {\frac{{AC}}{{AB}}} \right) = Mg\left[ {\frac{{1 - \frac{1}{{\sqrt 2 }}}}{{\frac{1}{2}}}} \right] \end{array}\)

\(\begin{array}{l} [\,AB = \ell \,\sin \,{45^ \circ } = \frac{\ell }{{\sqrt 2 }}\\ and\,AC = OC - OA = \ell  - \ell \cos {45^ \circ } = \ell \left( {1 - \frac{1}{{\sqrt 2 }}} \right)\\ Where\,\ell \, = length\,of\,the\,string.]\\  \Rightarrow F = Mg\,\left( {\sqrt 2  - 1} \right) \end{array}\)