Questions without answers in Applied Mechanics and Design

A horizontal disk has a radial frictionless slot in which a small block is confined to slide. The disk turns anticlockwise about its centre with a constant angular veloci...

A gear train with five gears is shown in the figure below. The number of teeth on each gear is $\mathrm{N}_{1}, \mathrm{~N}_{2}, \mathrm{~N}_{3}, \mathrm{~N}_{4}$, and $\...

In a single degree of freedom vibrating system with only viscous damping, the critical damping coefficient is $350 \mathrm{~N} \mathrm{~s} / \mathrm{m}$ and the damping c...

A closely coiled helical compression spring of mean coil diameter $D$ and wire diameter $d$, is loaded by an axial force $F$.The maximum shear stress developed in the wir...

The rotor of an aeroplane engine has a mass moment of inertia $1.0 \mathrm{~kg} \mathrm{~m}^{2}$. The engine rotates at a speed of $500$ RPM in the clockwise direction if...

A rectangular plate is perfectly welded to a gusset plate with parallel fillet weld joints as shown in the figure below. The length of the weld is $l$ and the fillet weld...

Worm gearsets are used for transmitting rotary motion betweennon-parallel and non-intersecting shaftsintersecting shaftsparallel shaftsnon-parallel and intersecting shaft...

A steel plate having yield strength of $550$ MPa , is subjected to biaxial state of stress as $\sigma_{x}=\sigma$ and $\sigma_{y}=-2 \sigma$. Using distortion energy theo...

A cantilever beam of length $L$ is subjected to a concentrated load $P$ and a moment $M$ as shown in the figure below. Neglecting the mass of the beam, which one of the f...

A $5$ kg mass is suspended at the free end of an overhanging massless beam, having a pin support and a roller support, as shown in the figure below. Young's modulus of th...

A block of $50$ kg mass is on an inclined plane. The block is connected to another hanging mass M by an inextensible massless string through two massless pulleys as shown...

A simply supported beam is subjected to an external point load P as shown in the figure below. The beam has a rectangular cross-section of $20 \mathrm{~mm} \times 45 \mat...

A rigid slender bar, AB, is sliding against two mutually perpendicular frictionless walls, as shown in the figure below. The velocity of A in the downward direction at a ...

A cylindrical pressure vessel made of steel has diameter of $3$ m and wall thickness of $15$ mm. For steel, Young's modulus and Poisson's ratio are $210$ GPa and $0.3$, r...

A welded square plate of $1 \mathrm{~m} \times 1 \mathrm{~m}$ is subjected to biaxial stress of magnitude $6.5$ MPa and $25$ MPa , as shown in the figure below. The ratio...

Suppose that with a pulley system, youneed to exert a force of 1,400 N to lifta heavy object. But without the pulleysystem, you need to exert 4,200 N tolift the object. W...

​​​​​In the context of balancing of rotating and reciprocating masses, which one of the following options is true?An unbalanced rigid rotor can be completely balanced usi...

​​​​A shaft carries a helical spur gear. Which one of the following bearings can NOT be used to support it?Angular contact bearingDouble-row ball bearingStraight roller b...

A block of mass $1 \: kg$ connected to a spring of stiffness $10 \mathrm{~N} \mathrm{~m}^{-1}$ is operating in a viscous medium such that the damping ratio (or damping fa...

​​​​​The system shown in the figure below consists of a cantilever beam (with flexural rigidity $E I$ and negligible mass), a spring (with spring constant $K$ and negligi...

The state of stress at a point is shown in the figure given below. Under plane stress assumption, the normal strain along the thickness direction $(\varepsilon_{z z})$ is...

A simply supported beam of length $1 \: \text{m}$ is subjected to a uniformly distributed bending moment of $1 \: \text{N m}$ per $\text{m}$ throughout the length as show...

A pair of spur gears is required to maintain a velocity ratio of $1: 2$. The module of the gears is $10 \: mm$ and the addendum is $10 \: mm$. If the operating pressure a...

An offset slider-crank mechanism is shown in the figure below. The length of the stroke of the slider is __________ $mm$ (rounded off to nearest integer).

Two plates of thickness $10 \: mm$ each are to be joined by a transverse fillet weld on one side and the resulting structure is loaded as shown in the figure below.If the...

​​​For a ball bearing, the fatigue life in millions of revolutions is given by $L=\left(\frac{C}{P}\right)^{n}$, where $\text{P}$ is the constant applied load and $\text{...

​​​​The change in kinetic energy $\Delta E$ of an engine is $300 \mathrm{~J}$, and minimum and maximum shaft speeds are $\omega_{\min }=220 \mathrm{rad} / \mathrm{s}$ and...

​​​​A ram in the form of a rectangular body of size $l=9 \mathrm{~m}$ and $b=2 \mathrm{~m}$ is suspended by two parallel ropes of lengths $7 \mathrm{~m}$. Assume the cent...

​​​​A linear spring-mass-dashpot system with a mass of $2 \mathrm{~kg}$ is set in motion with viscous damping. If the natural frequency is $15 \mathrm{~Hz}$, and the ampl...

​​​​Which one of the following failure theories is the most conservative design approach against fatigue failure?Soderberg lineModified Goodman lineGerber lineYield line