Applied Mathematics — First: Statics · Mathematics. These are 10 questions from the Magmo3 bank on this lesson, from easy to hard. Solve each one, then open "Show answer and explanation". Magmo3 has 70 questions on this lesson, each with an explanation.
The unit that measures the moment of a force is:
Correct answer: (A) N·m
Explanation: Step 1: Moment = force (newton, N) × distance (metre, m). Step 2: Its unit is newton × metre. ∴ The unit of a moment is N·m.
A force of magnitude 12 N acts at a perpendicular distance of 5 m from a point O. Find the magnitude of its moment about O.
Correct answer: (D) 60 N·m
Explanation: Step 1: Magnitude of a moment = force × perpendicular distance, M = F × d. Step 2: M = 12 × 5. Step 3: M = 60. ∴ The moment = 60 N·m.
A force produces a moment of 30 N·m about a point O. Keeping the same force, if the perpendicular distance is doubled, the new moment is:
Correct answer: (C) 60 N·m
Explanation: Step 1: M = F × d, so M is directly proportional to d. Step 2: Doubling d doubles the moment: M(new) = 2 × 30. Step 3: M(new) = 60. ∴ The new moment = 60 N·m.
A force F = 2i − 5j acts at the point A(3, 1), where lengths are in metres and forces in newtons. Find the moment vector of F about the point B(1, −2).
Correct answer: (A) −16k N·m
Explanation: Step 1: r = BA = A − B = (3 − 1, 1 − (−2)) = (2, 3). Step 2: M_B = r × F = (x·Fy − y·Fx) k = (2 × (−5) − 3 × 2) k. Step 3: M_B = (−10 − 6) k = −16k. ∴ M_B = −16k N·m (clockwise rotation about B).
About a point O, one force has a moment of +18 N·m and another has a moment of −7 N·m (anticlockwise positive). Find their total moment about O.
Correct answer: (A) 11 N·m anticlockwise
Explanation: Step 1: The total moment is the algebraic sum of the moments (anticlockwise positive). Step 2: M(total) = (+18) + (−7). Step 3: M(total) = +11 (anticlockwise). ∴ M(total) = 11 N·m anticlockwise.
A force of magnitude 20 N acts at the point A(4, 3), where lengths are in metres. Its line of action makes an angle of 30° with the positive x-axis, pointing up and to the right. Using Varignon's theorem, find the algebraic measure of its moment about the origin O.
Correct answer: (A) (40 − 30√3) N.m
Explanation: Components: Fx = 20 cos 30° = 10√3 N, Fy = 20 sin 30° = 10 N. Moment of Fy about O = +4 × 10 = 40 (anticlockwise); moment of Fx = −3 × 10√3 = −30√3 (clockwise). M_O = 40 − 30√3 ≈ −12 N.m, so the force turns clockwise about O. (40√3 − 30 comes from swapping sin and cos.)
Two forces act in a plane: F1 = (0, 5) N at the point (2, 0) m and F2 = (0, −5) N at the point (5, 0) m. Find the total moment of the two forces about the origin O.
Correct answer: (D) 15 N·m clockwise
Explanation: Step 1: Moment of F1 about O = (2)(5) − (0)(0) = 10. Step 2: Moment of F2 about O = (5)(−5) − (0)(0) = −25. Step 3: Total = 10 + (−25) = −15 (clockwise). ∴ M(total) = 15 N·m clockwise.
A force F = (4, 3) N acts at the point (x, 2) m. If its moment about the origin O is zero, find the value of x.
Correct answer: (D) 8/3 m
Explanation: Step 1: M = x·Fy − y·Fx = (x)(3) − (2)(4) = 3x − 8. Step 2: Set M = 0: 3x − 8 = 0. Step 3: 3x = 8, so x = 8/3. ∴ x = 8/3 m.
ABCD is a square of side 6 cm, labelled anticlockwise. Forces of 2, 3, 4 and 5 N act along AB, BC, CD and DA respectively (in the order of the letters), and a force of 4√2 N acts along AC. Find the sum of the moments of the forces about B.
Correct answer: (A) 30 N·cm anticlockwise
Explanation: Step 1: AB and BC pass through B (zero moment); CD: 4 × 6 = 24 and DA: 5 × 6 = 30, both anticlockwise. Step 2: B is at distance 6/√2 = 3√2 from AC, and the force A→C turns clockwise about B: 4√2 × 3√2 = 24 clockwise. ∴ Sum = 24 + 30 − 24 = 30 N·cm anticlockwise; 54 comes from ignoring the diagonal force.
A force of magnitude 15 N is inclined to the x-axis at an angle θ where cosθ = 4/5 and sinθ = 3/5. It acts at the point (0, 10) m. Find its moment about the origin O.
Correct answer: (A) 120 N·m clockwise
Explanation: Step 1: Components: Fx = 15 cosθ = 15(4/5) = 12, Fy = 15 sinθ = 15(3/5) = 9. Step 2: The point is (0, 10), so M = x·Fy − y·Fx = (0)(9) − (10)(12). Step 3: M = 0 − 120 = −120 (clockwise). ∴ M = 120 N·m clockwise.
The first 10 questions in every subject are free, each with an explanation.