Given, mass of the body, m=1kg Coefficient of static friction, µ=1/√3 Let's draw the free body diagram of the block
Using the condition of the equilibrium In x-direction, Fcosθ=f=φ=µN...(i) In y-direction, Fsinθ+N=mg ⇒N=mg−Fsinθ....(ii) Substituting the value of N in Eq. (i), we get F=
µmg
cosθ+µsinθ
⇒F=
µmg
√1+µ2
Substituting the values in the above equation, we get F=
1
√3
×10
√1+(
1
√3
)2
⇒F=5N Hence, the body move by applying minimum possible force of 5N. So, the value of F will be 5 .