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Applied mechanics

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Most Frequently Asked Questions

Top recurring IOE board exam questions for Applied mechanics with verified mark schemes, formula notation, and recurrence frequency.

Showing 30 of 30 top repeated questions

Forces Acting on Particle and Rigid Body

4 Questions

#1Repeated 3 Times[6 Marks]Forces Acting on Particle and Rigid Body

State and explain the fundamental principles of Newtonian mechanics and the principle of transmissibility with its limitations. State the equations of static equilibrium for 2D and 3D force systems acting on rigid bodies.

Appeared in:2081 Baishakh2080 Baishakh2076 Chaitra

#2Repeated 2 Times[4 Marks]Forces Acting on Particle and Rigid Body

State and prove Varignon's Theorem of moments.

Appeared in:2076 Chaitra2075 Chaitra

#3Repeated 2 Times[6 Marks]Forces Acting on Particle and Rigid Body

State and explain the principle of transmissibility of forces and equations of static equilibrium in 2D and 3D space. What are the limitations of the principle of transmissibility?

Appeared in:2082 Shrawan2081 Bhadra

#4Repeated 2 Times[8 Marks]Forces Acting on Particle and Rigid Body

State Lami's theorem. Three smooth cylinders of weight $W = 500\text{ N}$ each and radius $r = 100\text{ mm}$ are placed in a channel of width $360\text{ mm}$. Calculate the reactions at all contact points.

Appeared in:2082 Baishakh2079 Bhadra

Friction

4 Questions

#1Repeated 4 Times[6 Marks]Friction

Define angle of friction, angle of repose, and cone of friction. Explain the conditions for sliding versus tipping (overturning) of a rectangular block resting on an inclined plane.

Appeared in:2082 Baishakh2081 Baishakh2080 Baishakh2078 Bhadra

#2Repeated 2 Times[8 Marks]Friction

A uniform ladder of length $L$ and weight $W$ leans against a vertical wall and horizontal floor with friction. Determine the minimum coefficient of friction or maximum inclination angle to prevent slipping when a person ascends the ladder.

Appeared in:2080 Baishakh2076 Chaitra

#3Repeated 2 Times[6 Marks]Friction

Define angle of friction, angle of repose, and cone of friction. Derive the relationship between coefficient of static friction $\mu_s$, angle of friction $\phi$, and angle of repose $\theta$.

Appeared in:2082 Shrawan2081 Bhadra

#4Repeated 2 Times[8 Marks]Friction

Explain the working of a wedge and screw jack. Derive the expression for the effort $P$ required to raise a load $W$ using a square-threaded screw jack having mean diameter $d$, pitch $p$, and coefficient of friction $\mu$.

Appeared in:2082 Baishakh2078 Bhadra

Analysis of Simple Beams and Frames

6 Questions

#1Repeated 5 Times[10 Marks]Analysis of Simple Beams and Frames

For a given loaded beam or frame carrying concentrated point loads, uniformly distributed loads (UDL), and applied couples, calculate support reactions and draw the Axial Force Diagram (AFD), Shear Force Diagram (SFD), and Bending Moment Diagram (BMD). Locate points of contraflexure and determine maximum bending moment.

Appeared in:2082 Baishakh2081 Baishakh2080 Baishakh2078 Bhadra2076 Chaitra

#2Repeated 2 Times[4 Marks]Analysis of Simple Beams and Frames

Derive the differential relationship between distributed load $w(x)$, shear force $V(x)$, and bending moment $M(x)$: $\frac{dV}{dx} = -w(x)$ and $\frac{dM}{dx} = V(x)$.

Appeared in:2081 Baishakh2078 Bhadra

#3Repeated 2 Times[6 Marks]Analysis of Simple Beams and Frames

Explain the analysis of flexible cables supporting concentrated and uniformly distributed loads. Derive the cable tension and profile equations for parabolic and catenary cables.

Appeared in:2081 Baishakh2076 Chaitra

#4Repeated 2 Times[8 Marks]Analysis of Simple Beams and Frames

Differentiate between statically determinate and indeterminate trusses. Explain the Method of Joints and Method of Sections with their comparative merits and demerits.

Appeared in:2082 Shrawan2081 Bhadra

#5Repeated 2 Times[8 Marks]Analysis of Simple Beams and Frames

Derive the equations of a flexible cable carrying a uniformly distributed load over its horizontal span (parabolic cable). Obtain the formula for maximum tension $T_{\max}$ and total cable length.

Appeared in:2082 Baishakh2079 Baishakh

#6Repeated 2 Times[10 Marks]Analysis of Simple Beams and Frames

Draw the Axial Force Diagram (AFD), Shear Force Diagram (SFD), and Bending Moment Diagram (BMD) for a simply supported beam with an overhang carrying a combination of point load and uniformly distributed load (UDL). Locate the point of contraflexure.

Appeared in:2081 Bhadra2082 Baishakh

Analysis of Plane Trusses

1 Question

#1Repeated 5 Times[8 Marks]Analysis of Plane Trusses

Compute the forces developed in specified members of a pin-jointed plane truss (Warren truss, Pratt truss) using the Method of Joints and the Method of Sections. Indicate whether each member is in tension or compression.

Appeared in:2082 Baishakh2081 Baishakh2080 Baishakh2078 Bhadra2076 Chaitra

Centre of Gravity, Centroid, Moment of Inertia, and Mass Moment of Inertia

4 Questions

#1Repeated 4 Times[8 Marks]Centre of Gravity, Centroid, Moment of Inertia, and Mass Moment of Inertia

Determine the centroid $(\bar{x}, \bar{y})$, moment of inertia ($I_{xx}, I_{yy}$), and radius of gyration ($r_x, r_y$) of a standard composite structural section (T-section, I-section, angle section, or parabolic shaded area) about centroidal axes.

Appeared in:2082 Baishakh2081 Baishakh2080 Baishakh2078 Bhadra

#2Repeated 3 Times[4 Marks]Centre of Gravity, Centroid, Moment of Inertia, and Mass Moment of Inertia

State and prove the Parallel Axis Theorem for area moment of inertia ($I = I_G + A d^2$).

Appeared in:2080 Baishakh2078 Bhadra2076 Chaitra

#3Repeated 2 Times[6 Marks]Centre of Gravity, Centroid, Moment of Inertia, and Mass Moment of Inertia

Derive the expression for the moment of inertia and radius of gyration of a circular area of radius $R$ about its diametral axis using double integration.

Appeared in:2081 Bhadra2078 Bhadra

#4Repeated 2 Times[6 Marks]Centre of Gravity, Centroid, Moment of Inertia, and Mass Moment of Inertia

State Pappus-Guldinus theorems for determining surface area and volume of a body of revolution. Use the theorem to find the volume and surface area of a circular torus.

Appeared in:2082 Baishakh2080 Bhadra

Kinematics of Particles (Rectilinear and Curvilinear Motion)

4 Questions

#1Repeated 3 Times[6 Marks]Kinematics of Particles (Rectilinear and Curvilinear Motion)

The acceleration of a particle moving rectilinearly is defined by the relation $a = -10 x^{-2}$ (or $a = -kv$ or $a = 3t$). If the particle starts with specified initial conditions, determine its velocity, position, and total distance traveled.

Appeared in:2081 Baishakh2080 Baishakh2078 Bhadra

#2Repeated 3 Times[8 Marks]Kinematics of Particles (Rectilinear and Curvilinear Motion)

A projectile is launched from an initial elevation with velocity $v_0$ at an angle $\theta$ to the horizontal. Derive expressions for maximum height $H_{\max}$, horizontal range $R$, and time of flight $T$, and determine its velocity and strike angle on an inclined target.

Appeared in:2080 Baishakh2078 Bhadra2076 Ashwin

#3Repeated 2 Times[8 Marks]Kinematics of Particles (Rectilinear and Curvilinear Motion)

Derive expressions for radial and transverse components of velocity and acceleration of a particle moving along a plane curved path in polar coordinates ($r, \theta$).

Appeared in:2081 Bhadra2080 Baishakh

#4Repeated 2 Times[6 Marks]Kinematics of Particles (Rectilinear and Curvilinear Motion)

Two cars A and B travel in the same direction on a straight road. Car A starts from rest with constant acceleration $a_A = 2\text{ m/s}^2$. At the same instant, car B is $100\text{ m}$ ahead traveling with constant speed $v_B = 15\text{ m/s}$. Determine the time and location when car A overtakes car B.

Appeared in:2082 Baishakh2079 Bhadra

Kinetics of Particles: Force, Acceleration, Energy and Momentum

5 Questions

#1Repeated 3 Times[8 Marks]Kinetics of Particles: Force, Acceleration, Energy and Momentum

State the Principle of Linear Impulse and Momentum. Explain direct central and oblique impact between two bodies with coefficient of restitution $e = \frac{v_2' - v_1'}{v_1 - v_2}$ and solve an impact problem.

Appeared in:2081 Baishakh2080 Baishakh2078 Bhadra

#2Repeated 2 Times[8 Marks]Kinetics of Particles: Force, Acceleration, Energy and Momentum

State and prove the Work-Energy Principle for a particle ($T_1 + U_{1-2} = T_2$). State and explain the principle of conservation of mechanical energy for a system of connected particles with springs and gravity.

Appeared in:2078 Bhadra2076 Chaitra

#3Repeated 2 Times[6 Marks]Kinetics of Particles: Force, Acceleration, Energy and Momentum

Define angular momentum of a particle. Prove that the rate of change of angular momentum of a particle about a fixed point equals the sum of moments of external forces acting on it ($\sum M_O = \dot{H}_O$).

Appeared in:2080 Baishakh2078 Bhadra

#4Repeated 2 Times[6 Marks]Kinetics of Particles: Force, Acceleration, Energy and Momentum

State and prove the principle of conservation of linear momentum and impulse-momentum equation for a system of particles. Differentiate between perfectly elastic and inelastic impact.

Appeared in:2081 Bhadra2080 Bhadra

#5Repeated 2 Times[8 Marks]Kinetics of Particles: Force, Acceleration, Energy and Momentum

A bullet of mass $m = 20\text{ g}$ moving horizontally with velocity $v = 400\text{ m/s}$ strikes and embeds into a wooden block of mass $M = 3.98\text{ kg}$ suspended by a light string of length $L = 2\text{ m}$ (ballistic pendulum). Calculate the maximum vertical height and angular displacement of the pendulum.

Appeared in:2082 Baishakh2078 Bhadra

Kinematics and Kinetics of Rigid Body in Plane Motion, Energy and Momentum Methods

2 Questions

#1Repeated 3 Times[8 Marks]Kinematics and Kinetics of Rigid Body in Plane Motion, Energy and Momentum Methods

State D'Alembert's Principle for rigid bodies. Derive equations of planar motion for a rigid body undergoing general plane motion, showing decomposition into translational motion of center of mass ($F = ma_G$) and rotational motion about center of mass ($M_G = I_G \alpha$).

Appeared in:2080 Baishakh2078 Bhadra2076 Chaitra

#2Repeated 2 Times[6 Marks]Kinematics and Kinetics of Rigid Body in Plane Motion, Energy and Momentum Methods

Define Instantaneous Center of Zero Velocity (ICZV). Explain how the velocity of any point on a plane rigid body can be determined using ICZV with a neat diagram.

Appeared in:2082 Shrawan2081 Bhadra