Mechanical Engineering 2025 Paper I 50 marks Compulsory Calculate

Q1

(a) A gripper is shown in the figure. A horizontal force F = 50 N is applied to the handle of the lever at E. The mean diameter of the single square threaded screw at C and E is 25 mm and lead is 5 mm. Determine the clamping force developed at G. The coefficient of static friction is μs = 0·3. (10 marks) (b) The aluminium rod ABC having Young's modulus 70 GPa consisting of two cylindrical portions AB and BC, is to be replaced with a cylindrical steel rod DE with Young's modulus 200 GPa of same overall length. Determine minimum required diameter, d, of the steel rod if its vertical deformation is not to exceed the deformation of aluminium rod under the same load and if the allowable stress in the steel rod is not to exceed 165 MPa. (10 marks) (c) A tank shown in the figure is filled with compressed air under pressure of 8 MPa. A torque of magnitude T = 12 kNm is applied at the end. The tank has an inner diameter of 180 mm and thickness of wall 12 mm. Determine the maximum normal stress and maximum shearing stress in the tank considering the cylinder is thin. (10 marks) (d) With the help of a neat diagram, illustrate the microstructures of various phases of steel and exhibit the presence of the following: (10 marks) (i) Ferrite (ii) Austenite (iii) Cementite (iv) Pearlite (e) A pair of involute profile spur gears in mesh have to give a speed ratio of 2. The pressure angle is 20° and the module is 10 mm. The pinion has 24 teeth and drives the larger gear. If the addenda on pinion and gear wheels are equal to one module, determine: (10 marks) (i) length of path of contact, (ii) contact ratio, and (iii) angle of action of the pinion.

हिंदी में प्रश्न पढ़ें

(a) चित्र में एक पकड़ (ग्रिपर) दर्शाया गया है। लीवर के हस्ते (हैंडल) पर E पर एक क्षैतिज बल F = 50 N लगाया गया है। C तथा E पर एकल वर्ग चुड़ी वाले पेंच का औसत व्यास 25 mm तथा अग्रण (लीड) 5 mm है। G पर विकसित होने वाला बंधन बल (क्लैंपिंग फोर्स) निर्धारित कीजिए। स्थैतिक घर्षण गुणांक μs = 0·3 है। (10 अंक) (b) दो बेलनाकार भागों AB तथा BC से बनी 70 GPa यंग मापांक वाली एक ऐलुमिनियम छड़ ABC को एक 200 GPa यंग मापांक वाली समान समग्र लंबाई की बेलनाकार इस्पात छड़ DE के द्वारा प्रतिस्थापित किया जाना है। यदि इसका उद्वाधर विरूपण समान भार के अंतर्गत ऐलुमिनियम छड़ के विरूपण से अधिक न हो, एवं यदि इस्पात छड़ में स्वीकार्य प्रतिबल 165 MPa से अधिक न हो, तो इस्पात छड़ का न्यूनतम आवश्यक व्यास d निर्धारित कीजिए। (10 अंक) (c) चित्र में दर्शाई गई एक टंकी को 8 MPa के दबाव के तहत संपीडित वायु द्वारा भरा गया है। सिरे पर T = 12 kNm परिमाण का बल-आघूर्ण लगाया गया है। टंकी का आंतरिक व्यास 180 mm तथा दीवार की मोटाई 12 mm है। बेलन को पतला मानते हुए टंकी में अधिकतम सामान्य प्रतिबल तथा अधिकतम अपरूपण प्रतिबल निर्धारित कीजिए। (10 अंक) (d) एक साफ-सुथरे आरेख की सहायता से इस्पात के विभिन्न चरणों की सूक्ष्म संरचनाओं को चित्रित कीजिए तथा निम्नलिखित की उपस्थिति प्रदर्शित कीजिए: (10 अंक) (i) फेराइट (ii) ऑस्टेनाइट (iii) सीमेंटाइट (iv) पर्लाइट (e) एक जोड़ी प्रतिकेंद्रज प्रोफाइल में अंतर्नोजित स्पर गियर को 2 का गति अनुपात प्रदान करना है। दबाव कोण 20° है तथा प्रमात्रक (मॉड्यूल) 10 mm है। पिनियन में 24 दांते हैं तथा यह बड़े गियर को चलाती है। यदि पिनियन एवं गियर चक्रों पर युक्तक (ऐडेंडा) एक प्रमात्रक के बराबर है, तो निर्धारित कीजिए: (10 अंक) (i) संपर्क मार्ग की लंबाई, (ii) संपर्क अनुपात, और (iii) पिनियन का क्रिया कोण।

Evaluate your answer to this question → See all 2025 Mechanical Engineering questions

Directive word: Calculate

This question asks you to calculate. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

See our UPSC directive words guide for a full breakdown of how to respond to each command word.

How this answer will be evaluated

Approach

Calculate numerical solutions for all five parts with systematic derivations. For (a)-(c) and (e), show complete free-body diagrams, equilibrium equations, and step-by-step computations. For (d), draw neat microstructure diagrams with proper labelling. Allocate time proportionally: ~15% each for (a), (b), (c), (e) numerical parts and ~25% for (d) diagrams with four microstructures. Conclude each numerical part with final answers in proper units.

Key points expected

  • Part (a): Torque at screw = F × lever arm; thread angle tan(α) = lead/(π×dm); efficiency η = tan(α)/(tan(α+φ)); clamping force = (F×lever arm)×η/(dm/2 × tan(α+φ)) with φ = arctan(μs)
  • Part (b): Equate total deformation δ_al = δ_st; use δ = PL/AE for each segment; check stress constraint σ_st ≤ 165 MPa; solve for minimum d satisfying both conditions
  • Part (c): Hoop stress σ_h = pd/2t; longitudinal stress σ_l = pd/4t; shear stress due to torque τ = Tr/J; principal stresses σ_1,2 = (σ_h+σ_l)/2 ± √[((σ_h-σ_l)/2)²+τ²]; τ_max = (σ_1-σ_2)/2
  • Part (d): Four labelled diagrams showing: (i) BCC ferrite (α-Fe, soft, ductile), (ii) FCC austenite (γ-Fe, high temperature), (iii) orthorhombic cementite (Fe3C, hard, brittle), (iv) lamellar pearlite (alternating ferrite+cementite layers)
  • Part (e): Path of contact = (√(r_a1²-r_b1²) + √(r_a2²-r_b2²) - r_p sinφ)/cosφ; contact ratio = path of contact/(πm cosφ); angle of action = path of contact/r_p1
  • Correct application of thin-walled assumption for (c): d/t = 15 > 10 validates assumption
  • Proper unit conversions: GPa to MPa, mm to m, kNm to Nm throughout all calculations

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies: (a) square thread mechanics with friction angle, (b) series/parallel deformation equivalence with stress constraint, (c) combined thin-cylinder and torsion stress analysis with Mohr's circle or direct formula, (d) crystal structures and carbon content of each steel phase, (e) involute geometry with base circle and addendum circle distinctions.Uses correct basic formulas but minor errors in combined loading superposition for (c) or confuses thread types in (a); phase diagrams in (d) essentially correct but missing key features like carbon percentages.Fundamental errors: treats screw as frictionless in (a), ignores stress constraint in (b), uses thick-cylinder theory in (c), confuses ferrite with austenite structure in (d), or uses circular pitch instead of base pitch in (e).
Numerical accuracy20%10All five parts computed correctly: (a) clamping force ~400-500 N range with exact value, (b) d ≈ 28-32 mm satisfying both constraints, (c) σ_max ≈ 70-75 MPa and τ_max ≈ 35-40 MPa, (e) path of contact ~45-50 mm, contact ratio ~1.6-1.8. All intermediate steps shown with proper significant figures.Final answers in correct ballpark but arithmetic slips in 1-2 parts; unit conversion errors (e.g., GPa not converted to MPa in (b)) caught late but corrected; or stress constraint in (b) checked but not governing.Major computational errors: wrong thread efficiency in (a), deformation inequality reversed in (b), principal stress formula errors in (c), or gear ratio applied incorrectly in (e) giving contact ratio < 1.
Diagram quality20%10Part (d) shows four distinct, neat microstructure sketches: ferrite (equiaxed grains, BCC), austenite (FCC with twinning), cementite (needle-like or network), pearlite (clear lamellar structure with layer spacing indicated). For (a), (c), (e): FBD of gripper mechanism, stress element on cylinder wall, and gear mesh geometry with path of contact clearly drawn.Microstructures in (d) drawn but lacking clarity in distinguishing features; or numerical parts have minimal/no diagrams though requested implicitly by 'shown in figure'.No diagrams for (d) despite explicit instruction; or diagrams confuse phases (e.g., pearlite drawn as single phase, cementite as ferrite); completely missing FBDs for mechanism problems.
Step-by-step derivation20%10Each part shows complete logical flow: (a) torque → thread angle → friction angle → efficiency → axial force; (b) δ_al expression → δ_st expression → equate → solve d → verify σ; (c) individual stresses → stress transformation → principal stresses → maximum shear; (e) radii calculations → path of contact derivation → contact ratio formula.Derivations present but skips key steps (e.g., jumps from input torque to output force without efficiency; or states principal stress formula without showing stress element); some parts better developed than others.Final answers stated with minimal or no working; or working is disorganized with no clear problem-solving structure; incorrect formulas applied without justification.
Practical interpretation20%10Interprets results meaningfully: (a) self-locking condition check for gripper safety; (b) comments on weight savings vs stiffness in aerospace/structural replacement decisions; (c) identifies critical stress location for pressure vessel design per IS 2825; (d) relates microstructures to mechanical properties for steel selection (e.g., rails, gears); (e) discusses contact ratio > 1.2 for smooth transmission in Indian railway gearboxes.Brief mention of practical relevance in 2-3 parts but superficial; e.g., states 'higher contact ratio is better' without explaining why or relating to specific application.No interpretation provided; treats all parts as pure mathematical exercises with no engineering context or design implications mentioned.

Practice this exact question

Write your answer, then get a detailed evaluation from our AI trained on UPSC's answer-writing standards. Free first evaluation — no signup needed to start.

Evaluate my answer →

More from Mechanical Engineering 2025 Paper I