Recent questions and answers in Engineering Mechanics

Two identical blocks $\text{A}$ and $\text{B}$ are connected by a rigid rod. The blocks rest against vertical and horizontal planes, as shown in the figure. The coefficie...

Let $\phi$ be a scalar field, and $\boldsymbol{u}$ be a vector field. Which of the following identities is true for $\operatorname{div}(\phi \boldsymbol{u})$? $\operatorn...

A beam is subjected to a system of coplanar forces as shown in the figure. The magnitude of vertical reaction at Support $\text{P}$ is ______________________ $\text{N}$ (...

An undamped spring-mass system with mass $m$ and spring stiffness $k$ is shown in the figure. The natural frequency and natural period of this system are $\omega \; \text...

A uniform rod $KJ$ of weight $w$ shown in the figure rests against a frictionless vertical wall at the point $K$ and a rough horizontal surface at point $J.$ It is given ...

A horizontal force of $\text{P kN}$ is applied to a homogeneous body of weight $25$ $\text{kN}$, as shown in the figure. The coefficient of friction between the body and ...

A wedge $\text{M}$ and a block $\text{N}$ are subjected to forces $\text{P}$ and $\text{Q}$ as shown in the figure. If force $\text{P}$ is sufficiently large, then the bl...

A body floating in a liquid is in a stable state of equilibrium if its metacentre lies above its centre of gravitymetacentre lies below its centre of gravitymetacentre co...

A rigid weightless platform $\textbf{PQRS}$ shown in the figure ( not drawn to the scale) can slide freely in the vertical direction. The platform is held in position by ...

A simple mass-spring oscillatory system consists of a mass $m$, suspended from a spring of stiffness $k$. Considering $z$ as the displacement of the system at any time $t...

The kinematic indeterminacy of the plane truss shown in the figure is$11$$8$$3$$0$

An assembly made of a rigid arm $A-B-C$ hinged at end $A$ and supported by an elastic rope $C-D$ at end $C$ is shown in the figure. The members may be assumed to be weigh...

For the stress state (in MPa) shown in the figure, the major principal stress is $10$ MPa.The shear stress $\tau$ is$10.0$ MPa$5.0$ MPa$2.5$ MPa$0.0$ MPa

Consider the structural system shown in the figure under the action of weight $W$. All the joints are hinged. The properties of the members in terms of length ($L$), area...

A square plate is suspended vertically from one of its edges using a hinge support as shown in figure. A water jet of $20 \: mm$ diameter having a velocity of $10 \: m/s$...

A rigid member ACB is shown in the figure. The member is supported at A and B by pinned and guided roller supports, respectively. A force $\color{Red}{P}$ acts at $C$ as ...

An elastic bar of length $L$, uniform cross sectional area $A$, coefficient of thermal expansion $\alpha$, and Young’s modulus $E$ is fixed at the two ends. The temperatu...

Consider two axially loaded columns, namely, $1$ and $2$, made of a linear elastic material with Young’s modulus $2 \times 10^5$ MPa, square cross-section with side $10$ ...

A particle of mass $2$ kg is travelling at a velocity of $1.5$ m/s. A force $f(t) = 3t^2$ (in N) is applied to it in the direction of motion for a duration of $2$ seconds...

In a system, two connected rigid bars $AC$ and $BC$ are identical length, $L$ with pin supports at $A$ and $B$. The bars are interconnected at $C$ by a frictionless hinge...

Considering the symmetric of a rigid frame as shown below, the magnitude of the bending moment (in kNm) at P (preferably using the moment distribution method) is$170$$172...

Mathematical idealization of a crane has three bars with their vertices arranged as shown in the figure with a load of $80$ kN hanging vertically. The coordinates of the ...

A box of weight $100$ kN shown in the figure is to be lifted without swinging. If all forces are coplanar, the magnitude and direction $( \theta)$ of the force $(F)$ with...

If the following equation establishes equilibrium in slightly bent position, the mid-span deflection of a member shown in the figure is$$\frac{d^2y}{dx^2}+\frac{P}{EI}y=0...

The ultimate collapse load $(P)$ in terms of plastic moment $M_p$ by kinematic approach for a propped cantilever of length $L$ with $P$ acting at its mid-span as shown in...

The Poisson’s ratio is defined as$\begin{vmatrix} \dfrac{\text{axial stress}}{\text{lateral stress}} \end{vmatrix} \\$$\begin{vmatrix} \dfrac{\text{lateral strain}}{\text...

Two rigid bodies of mass $5$ kg and $4$ kg are at rest on a frictionless surface until acted upon by a force of $36$ N as shown in the figure. The contact force generated...

A cylinder of radius $250$ mm and weight, $W=10$ kN is rolled up an obstacle of height $50$ mm by applying a horizontal force $P$ at its centre as shown in the figure.All...