GATE

Q. In a four bar planar mechanism shown in the figure, AB = 5 cm, AD = 4 cm and DC = 2 cm. In the configuration shown, both AB and DC are perpendicular to AD. The bar AB rotates with an angular velocity of 10 rad/s. The magnitude of angular velocity (in rad/s) of […]

Q. A car having weight W is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height h from the ground, midway between the front and rear wheels. The distance between the front and rear wheels is l. The acceleration of the car is

Q. The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is Ans: 0.25 Sol: Given that 0 ≤ x ≤ 10 0

Q. A harmonic function is analytic if it satisfies the Laplace equation. If 𝑢(𝑥, 𝑦) = 2𝑥2 − 2𝑦2 + 4𝑥𝑦 is a harmonic function, then its conjugate harmonic function 𝑣(𝑥, 𝑦) is              (A) 4𝑥𝑦 − 2𝑥2 + 2𝑦2 + constant              (B) 4𝑦2 − 4𝑥𝑦 + constant              (C) 2𝑥2 − 2𝑦2 +

Q. The set of equations 𝑥 + 𝑦 + 𝑧 = 1 𝑎𝑥 – 𝑎𝑦 + 3𝑧 = 5 5𝑥 − 3𝑦 + 𝑎𝑧 = 6 has infinite solutions, if a = (A) −3 (B) 3 (C) 4 (D) −4 Ans: 4 Sol: ρ(A)=ρ(AB)< no.of variables|A|=0

Q. Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from O. Upon loading, the stress-strain curve passes through initial yield point at P, and then strain hardens to point Q, where the loading was stopped. From point Q, the

Q. Air of mass 1 kg, initially at 300 K and 10 bar, is allowed to expand isothermally till it reaches a pressure of 1 bar. Assuming air as an ideal gas with gas constant of 0.287 kJ/kg.K, the change in entropy of air (in kJ/kg.K, round off to two decimal places) is   Ans:

Q. During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of +140 MPa, and a minimum stress of −70 MPa. The R-ratio (minimum stress to maximum stress) for this cyclic loading is Sol:

Q. A solid cube of side 1 m is kept at a room temperature of 32 °C. The coefficient of linear thermal expansion of the cube material is 1×10-5 / °C and the bulk modulus is 200 GPa. If the cube is constrained all around and heated uniformly to 42 °C, then the magnitude of

Q. A cylindrical rod of diameter 10 mm and length 1.0 m is fixed at one end. The other end is twisted by an angle of 10° by applying a torque. If the maximum shear strain in the rod is px10-3, then p is equal to (round off to two decimal places). Sol: