Torque from angled force on lever arm

Steps:

• Torque τ = F × perpendicular distance from pivot to line of force action.
• Perpendicular distance = d × sinθ, where θ=45° is angle between force and handle (lever arm).
• Sin45° = 1/√2.
• Thus, τ = F × d × (1/√2) = Fd/√2.

Why A is correct:

• Follows torque formula τ = r F sinθ, with r=d and θ=45°, so sin45°=1/√2 yields Fd/√2.

Why the others are wrong:

• B: Assumes θ=90° (sin90°=1) for maximum torque, ignoring the 45° angle.
• C: Incorrectly uses sin(45° inverse) or cos45°, overestimating by √2 factor.
• D: Doubles the value without basis, perhaps confusing with another angle or vector component.

Final answer: A