List of top Applied Mechanics and Design Questions

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 x_A = 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).

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)

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).

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).

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 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).

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).

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 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

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 w_min = 220 rad/s and w_max = 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

The radius of mohr's circle of stress of a strained element is 20 N/mm2 and minor principle tensile stress is 10 N/mm2 the major principle stress is

If a circular shaft is subjected to a torque T and a bending moment M, the ratio of maximum shear stress to maximum bending stress given by:

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The cross-sections of the shaft which are plane before twist, remain plane during and after twist.
Reasons (R): The twisting moment does not vary with the radius of the shaft.
In the light of the above statements, choose the most appropriate answer from the options given below:

Sensor used to measure the speed of rotating shaft is called:

A solid circular shaft of diameter 'd' is subjected to a combined bending moment 'M' and torque "T. The material property to be used for designing the shaft using the relation \(\frac{16}{\pi d^3} \times \sqrt{M^2+T^2}\) is:

A solid circular shaft is required to transmit a torque of 100 Nm. If the permissible shear stress for the material is 180 MPa, the diameter of a shaft in mm is:
(Assume FOS as 2)

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)

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)