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Mechanical Engineering 2025 Paper I 50 marks Compulsory Calculate

Paper I — 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…

(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)
(i)

With the help of a neat diagram, illustrate the microstructures of various phases of steel and exhibit the presence of the following: (10 marks) Ferrite

(ii)

Austenite

(iii)

Cementite

(iv)

Pearlite

(e)
(i)

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) 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)
(i)

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) फेराइट

(ii)

ऑस्टेनाइट

(iii)

सीमेंटाइट

(iv)

पर्लाइट

(e)
(i)

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) संपर्क मार्ग की लंबाई,

(ii)

संपर्क अनुपात, और

(iii)

पिनियन का क्रिया कोण।

Q1 of the 2025 UPSC Mains Mechanical Engineering Paper I, as printed
The question as printed in the 2025 Mechanical Engineering paper
Model answer coming soon See all 2025 Mechanical Engineering questions

The figure this question refers to, in words

The question paper is a scan and the diagram did not survive as text. This is the figure as read from the original page — every component, value and label — so the question can be worked from the text below.

(a) A schematic diagram of a mechanical gripper mechanism. The assembly consists of a C-shaped frame with a horizontal top arm and a horizontal bottom arm. A vertical square-threaded screw passes through the top arm at point C and the bottom arm at point D. The screw extends downwards to a horizontal handle lever at point E. A horizontal force F is applied to the end of the handle at E. The handle length from the screw axis to point E is 125 mm. The top arm has a pivot point A and a clamping point C. The bottom arm has a pivot point B and a connection point D. The distance from the clamping point G (located at the left end of the top arm) to the pivot A is 200 mm. The distance from the pivot A to the screw axis at C is 200 mm. The screw is single square threaded with a mean diameter of 25 mm and a lead of 5 mm. The coefficient of static friction is 0.3. The applied force F is 50 N.

(b) Two vertical rod configurations are shown side-by-side. On the left is a stepped aluminium rod ABC fixed at the bottom end C. It consists of two cylindrical sections: the upper section AB has a length of 300 mm and a diameter of 38 mm; the lower section BC has a length of 450 mm and a diameter of 56 mm. A vertical downward force of 125 kN is applied at the top end A. On the right is a uniform cylindrical steel rod DE fixed at the bottom end E. It has a uniform diameter labeled 'd' and a total length equal to the sum of the lengths of sections AB and BC (750 mm). A vertical downward force of 125 kN is applied at the top end D.

(c) A vertical cylindrical tank with a flat top and bottom, mounted on a square base plate. A curved arrow labeled 'T' is drawn around the top rim of the cylinder, indicating a torque applied about the vertical axis. The cylinder is depicted with a shaded surface to suggest a 3D perspective.

What "Calculate" is asking you to do

Apply the standard formula or schedule to data the question has already supplied — a table of readings, cost records, a balance sheet — and produce the number. The method is rarely in doubt; the marks sit in the named intermediate quantities, each of which has to appear as a labelled line.

Structure that answers it

Data as given → formula or standard treatment, named → substitution → each intermediate, labelled → result with units

Where marks are lost

Omitting an intermediate the marking scheme pays for separately, or rounding at an intermediate line so the final figure drifts. In commerce and accountancy, any figure in a statement that no numbered working note supports is treated as unearned.

All UPSC directive words, compared →

How this answer will be evaluated

Approach

(a) calculate: given > formula > substitution > result with units > interpretation | (b) calculate: given > formula > substitution > result with units > interpretation | (c) calculate: given > formula > substitution > result with units > interpretation | (d) describe: define > structure or process in order > labelled diagram > significance | (e) calculate: given > formula > substitution > result with units > interpretation Full marks: Rigorous application of governing equations with clear diagrams and physical interpretation.

Key points expected

  • Free body diagram of lever CDE
  • Torque equilibrium at pivot D
  • Screw friction formula (square thread)
  • Moment equilibrium at pivot A
  • Deformation calculation for Al rod (AB+BC)
  • Equating steel deformation to Al deformation
  • Stress constraint check (165 MPa)
  • Final diameter selection based on both criteria

Evaluation rubric

Each sub-part is marked on its own, against the marks and word limit printed on the paper.

  1. (a) Determine the clamping force developed at G. 10 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • Free body diagram of lever CDE
    • Torque equilibrium at pivot D
    • Screw friction formula (square thread)
    • Moment equilibrium at pivot A

    Loses marks

    • Ignoring friction in screw calculation
    • Incorrect moment arm identification

    Earns more

    • Correct calculation of friction angle
    • Clear identification of reaction forces

    Extra mark

    • Check for self-locking condition
  2. (b) Determine minimum required diameter d of the steel rod. 10 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • Deformation calculation for Al rod (AB+BC)
    • Equating steel deformation to Al deformation
    • Stress constraint check (165 MPa)
    • Final diameter selection based on both criteria

    Loses marks

    • Ignoring the stress limit
    • Using wrong Young's modulus values

    Earns more

    • Correct area calculation for each segment
    • Clear comparison of deformation vs stress limits

    Extra mark

    • Explicit statement of which criterion governs
  3. (c) Determine maximum normal and shearing stress in the tank. 10 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • Hoop and longitudinal stress formulas
    • Torsional shear stress calculation
    • Principal stress determination
    • Maximum shear stress calculation

    Loses marks

    • Using inner radius instead of mean
    • Ignoring torsional shear stress

    Earns more

    • Correct use of mean radius for thin wall
    • Clear stress element diagram

    Extra mark

    • Mohr's circle construction
  4. (d) Illustrate microstructures of steel phases. 10 marks

    describe— define → structure or process in order → labelled diagram → significance

    Must cover

    • Diagram of Ferrite (BCC)
    • Diagram of Austenite (FCC)
    • Diagram of Cementite (Fe3C)
    • Diagram of Pearlite (lamellar)

    Loses marks

    • Confusing Ferrite and Austenite structures
    • Missing any of the four phases

    Earns more

    • Correct crystal structure labels
    • Clear distinction between phases

    Extra mark

    • Mention of carbon content for each
  5. (e) Determine path of contact, contact ratio, and angle of action. 10 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • Gear geometry calculations (pitch radii)
    • Path of contact formula
    • Contact ratio calculation
    • Angle of action derivation

    Loses marks

    • Incorrect module application
    • Confusing pressure angle with helix angle

    Earns more

    • Correct calculation of base circle radii
    • Clear definition of contact ratio

    Extra mark

    • Diagram of gear meshing

Model answer coming soon

Every evaluation on this site is marked against a verified model answer. This question's answer is still being written; evaluation opens the moment it lands.

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