List of top Applied Mechanics and Design Questions asked in GATE Metallurgy

A vibratory system consists of mass m, a vertical spring of stiffness 2k and a horizontal spring of stiffness k. The end A of the horizontal spring is given a horizontal motion xA = αsinwt. The other end of the spring is connected to an inextensible rope that passes over two massless pulleys as shown. Assume m = 10 kg, k = 1.5 kN/m, and neglect friction. The magnitude of critical driving frequency for which the oscillations of mass m tend to become excessively large is ____rad/s (answer in integer).
vibratory system consists of mass m, a vertical spring of stiffness 2k and a horizontal spring of stiffness k
A horizontal beam of length 1200mm is pinned at the left end and is resting on a roller at the other end as shown in the figure. A linearly varying distributed load is applied on the beam. The magnitude of maximum bending moment acting on the beam is _____N.m. (round off to 1 decimal place)
A horizontal beam of length 1200mm is pinned at the left end and is resting on a roller at the other end
Which one of the following failure theories in the most conservative design approach against fatigue failure
The figure shows a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an angle a = 60° with the horizontal. The closed vessel has a wall thickness of 10mm and diameter of 2m. When subjected to an internal pressure of 200 kPa, the magnitude of the normal stress acting on the weld is ____MPa (rounded off to 1 decimal place).
a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an angle a = 60°
At the instant when OP is vertical and AP is horizontal, the link OD is rotating counter clockwise at a constant rate w=7rad/s. Pin P on link OD slides in the slot BC of link ABC which is hinged at A, and causes a clockwise rotation of the link ABC. The magnitude of angular velocity of link ABC for this instant is _____rad/s (rounded off to 2 decimal places).
OP is vertical and AP is horizontal, the link OD is rotating counter clockwise at a constant rate
A band brake shown in the figure has a coefficient of friction of 0.3. The band can take a maximum force of 1.5 kN. The maximum braking force (F) that can be safely applied is _____N (rounded off to the nearest integer).
A band brake shown in the figure has a coefficient of friction of 0.3
A solid massless cylindrical member of 50 mm diameter is rigidly attached at one end, and is subjected to an axial force P = 100 kN and a torque T = 600 N. m at the other end as shown. Assume that the axis of the cylinder is normal to the support. Considering distortion energy theory with allowable yield stress as 300 MPa, the factor of safety in the design is _____ (rounded off to 1 decimal place).
solid massless cylindrical member of 50 mm diameter is rigidly attached at one end
A three-hinge arch ABC in the form of a semi-circle is shown in the figure. The arch is in static equilibrium under vertical loads of P = 100 kN and Q = 50 kN. Neglect friction at all the hinges. The magnitude of the horizontal reaction at B is ____KN (rounded off to 1 decimal place).
A three-hinge arch ABC in the form of a semi-circle
The Levai type-A train illustrated in the figure has gears with module m = 8 mm/tooth. Gears 2 and 3 have 19 and 24 teeth respectively. Gear 2 is fixed and internal gear 4 rotates at 20 rev/min counter-clockwise. The magnitude of angular velocity of the arm is _____rev/min. (rounded off to 2 decimal places)
The Levai type-A train illustrated in the figure has gears with module m = 8 mm/tooth
The phases present in pearlite are
A rigid massless tetrahedron is placed such that vertex O is at the origin and the other three vertices A, B, and C lie on the coordinate axes as shown in the figure. The body is acted on by three point loads, of which one is acting at A along x-axis and another at point B along y-axis. For the body to be in equilibrium, the third point load acting at point O must be
A rigid massless tetrahedron is placed such that vertex O is at the origin
Which one of the following failure theories is the most conservative design approach against fatigue failure?
The change in kinetic energy ΔE of an engine is 300 J, and minimum and maximum shaft speeds are wmin = 220 rad/s and wmax = 280 rad/s, respectively. Assume that the torque-time function is purely harmonic. To achieve a coefficient of fluctuation of 0.05, the moment of inertia (in kg.m2) of the flywheel to be mounted on the engine shaft is
A linear spring-mass-dashpot system with a mass of 2kg is set in motion with viscous damping. If the natural frequency is 15Hz, and the amplitudes of two successive cycles measured are 7.75mm and 7.20mm, the coefficient of viscous damping (in N.s/m) is
A solid massless cylindrical member of 50 mm diameter is rigidly attached at one end, and is subjected to an axial force, P = 100 kN and torque T = 600 Nm at the other end as shown. Assume that the axis of the cylinder is normal to the support. considering distortion energy theory with allowable yield stress as 300 MPa. The factor of safety in the design is _____ (Round of one decimal place)

A horizontal beam of length 1200 mm is pinned at the left end and is resting on the roller at the other end as shown in the figure. A linearly varying distributed load is applied on the beam. The magnitude of maximum bending moment acting on the beam is _____ Nm (Round off to one decimal place)

A horizontal beam of length 1200 mm is pinned at the left

For a ball bearing, the fatigue life in million revolutions is given by L=(C/P)n where P is the constant applied load and C is the basic dynamic load rating. Which one of the following statements is true
A band brake shown in the figure has a coefficient of friction of 0.3. The band can take a maximum force of 1.5 kN. The maximum braking force (F) that can be safety applied is ______ N. (Answer in integers)