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GATE 2016 Set 1
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1. GATE 2016- Set 1 By: Lohit K Yadav

2. A solid disc with radius a is connected to a spring at a point d above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is Mand the spring corstant is K.. The polar moment of inertia for the disc about its centre is J = Ma'/2The natural frequency of this system in rad/s is given by

3. M, J 2K (a+ d)2 3Ma2 (B) 2K 3M (C) J2K(a+d) K(a+ Ma2 Ma2

4. Upin od 18

5. k (a+d) 2 k Caid)

6. The principal stresses at a point inside a solid object are sl-100 MPa, s2 = 100 MPa and s3 o MPa. The yield strength of the material is 200 MPa. The factor of safety calculated using Tresca (maximum shear stress) theory is n, and the factor of sa calculated Which one of the following relations is TRUE? (A3/2)n (C) nT-n on Mises imum distortional energy) theorv is n.

7. IVn? Solz 3-G. 27 77-2

8. Sot [(r.ef. (n + (5.9"): 2 (20 ) loot 2 2

9. An inverted U-tube manometer is used to measure the pressure difference between two pipes A and B, as shown in the figure. Pipe A is carrying oil (specific gravity:- 0.8) and pipe B is carrying water. The densiti water The pressure difference between pipes A and B is Acceleration due to gravity g = 10 m/s2. kPa Air 80 mm 200 mm r and Water kg/m3 and 1000 100 mm A oil g/m3, respectively.

10. o 08