Assistant Engineer (Kerala Water Authority) — Kerala PSC PYQ Practice with Answers

Correct answer (Option A):\nThe stiffness (k) of a helical spring depends on its geometry and material properties. For an open-coil helical spring, the mechanical stiffness formula incorporates the mean coil diameter (D) raised to the third power in the denominator.\n\nFormula:\nk = (G × d⁴) / (8 × D³ × n)\n\nGiven this structural relationship, the stiffness is inversely proportional to the cube of the mean coil diameter, meaning it decreases drastically as the mean coil diameter increases. Therefore, Option A is the correct response.\n\nWhy others are wrong:\nOption B is wrong because stiffness is directly proportional to the fourth power of the wire diameter (d⁴), not inversely proportional. Option C is wrong because stiffness is directly proportional to the shear modulus of the wire material (G). Option D is wrong because the shear modulus, rather than the standard elastic modulus (E), governs structural twisting mechanics under axial loads.\n\nStudy tip:\nMemorize the standard helical spring stiffness parameters. Note that mean coil diameter (D) sits firmly in the denominator, while wire diameter (d) sits in the numerator.

Correct answer (Option A):\nAn influence line represents the variation of a specific structural response (like shear force or bending moment) at a fixed section as a unit load travels across a structural member. For a simply supported beam, the influence line diagram for the bending moment at any internal section is strictly linear, forming a distinct triangle with its apex situated directly at the section under consideration. Option A is correct.\n\nWhy others are wrong:\nOption B is incorrect because a parabola represents the bending moment diagram shape under a uniform dead or live load, not an influence line diagram driven by a moving unit point load. Option C is incorrect because a rectangular layout does not track the changing moment leverage as a load shifts. Option D is partially incomplete because while the lines are straight, they intersect to form a distinct geometric triangle profile across the span.\n\nStudy tip:\nRemember that for all statically determinate beams, influence lines for structural internal actions like bending moment and shear force always consist entirely of straight lines forming linear shapes such as triangles.

Correct answer (Option C):\nA three-hinged arch features two hinge supports at the abutments and a third internal hinge typically located at the crown. This structural arrangement introduces a total of four unknown reactive components (two horizontal and two vertical forces). The analyst can utilize the three standard global equations of static equilibrium along with an extra independent equations of condition (the internal bending moment equals zero at the crown hinge).\n\nEquations available: 3 + 1 = 4\nUnknown components: 4\n\nSince the number of independent equilibrium equations exactly equals the number of unknown support reactions, the system is classified as statically determinate. Option C is correct.\n\nWhy others are wrong:\nOptions A and B are incorrect because no extra redundant forces remain, meaning the system is not indeterminate. Option D is incorrect because a three-hinged arch provides a completely stable mechanism under general structural loading configurations.\n\nStudy tip:\nContrast this with a two-hinged arch, which lacks the internal crown hinge and is consequently statically indeterminate to the first degree ($D_s = 1$).

Correct answer (Option A):\nTo equate pressure heads between two fluids, we utilize the relationship where fluid pressure remains identical at the base of both columns.\n\nFormula: P = ρ₁ × g × h₁ = ρ₂ × g × h₂\nSimplifying gives: s₁ × h₁ = s₂ × h₂\n\nGiven values:\nSpecific gravity of water ($s_w$) = 1\nPressure head of water ($h_w$) = 136 m\nSpecific gravity of mercury ($s_m$) = 13.6\n\nStep 1: 1 × 136 = 13.6 × $h_m$\nStep 2: $h_m$ = 136 / 13.6\nStep 3: $h_m$ = 10 m\n\nAnswer: 10 meters of mercury. Option A is correct.\n\nWhy others are wrong:\nOption B (100) is mathematically incorrect due to a positional decimal miscalculation. Option C (13.6) represents the specific gravity of mercury itself, not the structural height. Option D (1) is wrong because it fails to satisfy the balanced hydrostatic pressure head equation.\n\nStudy tip:\nAlways remember that the specific gravity of mercury is exactly 13.6. Converting any water head to a mercury head simply requires dividing the water column height by 13.6.

Correct answer (Option B):\nThe specific energy loss ($E_L$) in a hydraulic jump occurring within a horizontal rectangular channel is computed explicitly using the sequent depths before and after the jump.\n\nFormula: $E_L$ = ($y_2$ - $y_1$)³ / (4 × $y_1$ × $y_2$)\n\nGiven values:\n$y_2$ = 1.5 m\n$y_1$ = 0.5 m\n\nStep 1: Numerator = (1.5 - 0.5)³ = (1.0)³ = 1.0\nStep 2: Denominator = 4 × 0.5 × 1.5 = 2.0 × 1.5 = 3.0\nStep 3: $E_L$ = 1.0 / 3.0\nStep 4: $E_L$ = 0.333 m\n\nAnswer: About 0.33 m. Option B is correct.\n\nWhy others are wrong:\nOptions A (3 m), C (1 m), and D (1.5 m) are mathematically invalid values that arise if one fails to apply the cubed subtraction or omits the product multiplier in the denominator.\n\nStudy tip:\nEnsure you track which depths are placed where. The top is the cube of the difference, while the bottom is four times the mathematical product of the two depths.