Engineering Mechanics — Part 1 MCQs with Explanations

To find the resultant of two equal forces P making an angle θ, we use the formula for the resultant of two forces: Resultant $$R$$ = $$2{\text{P}}\cos \frac{\theta }{2}$$ Here’s the derivation: - The two forces P are equal in magnitude and form an angle θ with each other. - The magnitude of the resultant force is given by $$2{\text{P}}\cos \frac{\theta }{2}$$ where $$ \frac{\theta }{2}$$ is the angle between one of the forces and the resultant. The other options involve sine, tangent, or cotangent functions, which do not correctly represent the magnitude of the resultant in this context.

Moment of inertia for a circular section about an axis perpendicular to the section is given by $$\frac{{\pi {{\text{d}}^4}}}{{32}}$$, where d is the diameter of the circle. Therefore, the correct answer is Option C .

The algebraic sum of the resolved parts of a number of forces in a given direction is equal to the resolved part of their resultant in the same direction. This is known as the Principle of resolution of forces . Here's the explanation: The Principle of resolution of forces states that when you have multiple forces acting in different directions, you can break them down or resolve them into their individual components along a specific direction. The algebraic sum (taking into account the signs of forces in that direction) of these resolved components will be equal to the resolved part of their resultant force in the same direction. This principle is a fundamental concept in engineering mechanics and is often used to simplify the analysis of complex force systems. So, the correct answer is Option B: Principle of resolution of forces .

Understanding the Question: Imagine a simple machine like a pulley system. It helps you lift heavy objects with less effort. We have a weight (load) of 1000 N that needs to be lifted. We only need to apply an effort of 80 N to lift it. The velocity ratio (VR) is 20. This tells us how much the machine multiplies the effort. A VR of 20 means the effort moves 20 times the distance the load moves. Mechanical Advantage (MA): The machine's mechanical advantage (MA) shows how much it multiplies the effort. We calculate MA by dividing the load by the effort: MA = Load / Effort = 1000 N / 80 N = 12.5 Efficiency: Efficiency tells us how effective the machine is. It's the ratio of MA to VR: Efficiency = (MA / VR) * 100% = (12.5 / 20) * 100% = 62.5% Reversible vs. Non-reversible Machines: A reversible machine has an efficiency greater than 50%. It can work in the reverse direction without extra help. For example, it can both lift a weight and lower it smoothly. A non-reversible machine has an efficiency less than 50%. To reverse it (lower the weight), you might need to apply an external force. Answer: Since the efficiency (62.5%) is greater than 50%, the machine is reversible . The correct option is A .

Equal to is the correct answer to “A framed structure is perfect, if the number of members are __________ (2j - 3), where j is the number of joints.”. This question is standard in competitive examination syllabi for Engineering Mechanics.

$$\sqrt {{{\left( {\sum {\text{V}} } \right)}^2} + {{\left( {\sum {\text{H}} } \right)}^2}} $$ is the correct answer to “If a number of forces are acting at a point, their resultant is given by”. This question is standard in competitive examination syllabi for Engineering Mechanics.

$${\text{a}} = \alpha {\text{r}}$$ is the correct answer to “The linear acceleration (a) of a body rotating along a circular path of radius (r) with an angular acceleration of $$\alpha $$ rad/s 2 , is”. This question is standard in competitive examination syllabi for Engineering Mechanics.

$${I_{\text{P}}} = {I_{\text{G}}} + {\text{A}}{{\text{h}}^2}$$ is the correct answer to “According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through center of gravity (i.e. $${I_{\text{P}}}$$) is given by (where, A = Area of the section, $${I_{\text{G}}}$$ = Moment of inertia of the section about an axis passing through its C.G. and h = Distance between C.G. and the parallel axis.)”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Static friction is the correct answer to “The friction experienced by a body, when at rest, is known as”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Potential energy is the correct answer to “The energy possessed by a body, for doing work by virtue of its position, is called”. This question is standard in competitive examination syllabi for Engineering Mechanics.

All of the above is the correct answer to “For any system of coplanar forces, the condition of equilibrium is that the”. This question is standard in competitive examination syllabi for Engineering Mechanics.

One-third of the total height above base is the correct answer to “Center of gravity of a thin hollow cone lies on the axis at a height of”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Both (A) and (B) is the correct answer to “The time of flight of a projectile on downward inclined plane depends upon”. This question is standard in competitive examination syllabi for Engineering Mechanics.

100 is the correct answer to “In a single threaded worm and worm wheel, the number of teeth on the worm is 50. The diameter of the effort wheel is 100 mm and that of load drum is 50 mm. The velocity ratio is”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Equal to is the correct answer to “The potential energy of a vertically raised body is __________ the kinetic energy of a vertically falling body.”. This question is standard in competitive examination syllabi for Engineering Mechanics.

$$\frac{{{{\text{m}}_1}{{\text{m}}_2}{\text{g}}\left( {1 + \sin \alpha } \right)}}{{{{\text{m}}_1} + {{\text{m}}_2}}}$$ is the correct answer to “A block of mass m 1 , placed on an inclined smooth plane is connected by a light string passing over a smooth pulley to mass m 2 , which moves vertically downwards as shown in the below figure. The tension in the string is”. This question is standard in competitive examination syllabi for Engineering Mechanics.

$$\frac{\pi }{{64}}\left( {{{\text{D}}^4} - {{\text{d}}^4}} \right)$$ is the correct answer to “Moment of inertia of a hollow circular section, as shown in the below figure about X-axis, is”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Like parallel forces is the correct answer to “The forces, whose lines of action are parallel to each other and act in the same directions, are known as”. This question is standard in competitive examination syllabi for Engineering Mechanics.

sinθ is the correct answer to “The velocity ratio in case of an inclined plane inclined at angle 'θ' to the horizontal and weight being pulled up the inclined plane by vertical effort is”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Increase is the correct answer to “A block of mass 20 kg lying on a rough horizontal plane is connected by a light string passing over a smooth pulley to another mass 5 kg, which can move freely in the Vertical direction, as shown in the below figure. The tension in the string will ___________ with the increase in coefficient of friction.”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Greater than is the correct answer to “The skidding away of the vehicle on a level circular path can be avoided if the force of friction between the wheels and the ground is __________ the centrifugal force.”. This question is standard in competitive examination syllabi for Engineering Mechanics.

0° and 180° is the correct answer to “The angle between two forces when the resultant is maximum and minimum respectively are”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Load lifted to the effort applied is the correct answer to “The mechanical advantage of a lifting machine is the ratio of”. This question is standard in competitive examination syllabi for Engineering Mechanics.

All of the above is the correct answer to “The efficiency of a lifting machine is the ratio of”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Strain energy is the correct answer to “When the spring of a watch is wound, it will possess”. This question is standard in competitive examination syllabi for Engineering Mechanics.

$$\frac{1}{{2\pi }}\sqrt {\frac{{{\text{gh}}}}{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}} $$ is the correct answer to “The frequency of oscillation of a compound pendulum is (where k G = Radius of gyration about the centroidal axis and h = Distance between the point of suspension and C.G. of the body.)”. This question is standard in competitive examination syllabi for Engineering Mechanics.

$$\omega \sqrt {{{\text{r}}^2} - {{\text{y}}^2}} $$ is the correct answer to “The velocity of a particle (v) moving with simple harmonic motion, at any instant is given by (where, r = Amplitude of motion and y = Displacement of the particle from mean position.)”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Does not change is the correct answer to “If a given force (or a given system of forces) acting on a body __________ the position of the body, but keeps it in equilibrium, then its effect is to produce internal stress in the body.”. This question is standard in competitive examination syllabi for Engineering Mechanics.

$$\frac{{{{\text{u}}^2}{{\sin }^2}\alpha }}{{2{\text{g}}}}$$ is the correct answer to “The maximum height of a projectile on a horizontal plane, is”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Limiting friction is the correct answer to “The maximum frictional force which comes into play when a body just begins to slide over another surface is called”. This question is standard in competitive examination syllabi for Engineering Mechanics.

$$\frac{{2{\text{m}}{{\text{r}}^2}}}{5}$$ is the correct answer to “The moment of inertia of a solid sphere of mass ‘m’ and radius ‘r’ is”. This question is standard in competitive examination syllabi for Engineering Mechanics.

$$\frac{{{\text{g}}\left( {{{\text{m}}_1} - {{\text{m}}_2}} \right)}}{{{{\text{m}}_1} + {{\text{m}}_2}}}$$ is the correct answer to “Two bodies of masses m 1 and m 2 are hung from the ends of a rope, passing over a frictionless pulley as shown in the figure below. The acceleration of the string will be”. This question is standard in competitive examination syllabi for Engineering Mechanics.

All of these is the correct answer to “Which of the following are vector quantities”. This question is standard in competitive examination syllabi for Engineering Mechanics.

0.5 mv2 is the correct answer to “When a body of mass 'm' attains a velocity 'v' from rest in time 't', then the kinetic energy of translation is”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Greater than is the correct answer to “If two bodies having masses m 1 and m 2 (m 1 > m 2 ) have equal kinetic energies, the momentum of body having mass m 1 is _________ the momentum of body having mass m 2 .”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Decrease is the correct answer to “In the shown figure, if the angle of inclination of the plane is increased, then acceleration of the system will”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Twice the area of the triangle is the correct answer to “Three forces acting on a rigid body are represented in magnitude, direction and line of action by the three sides of a triangle taken in order. The forces are equivalent to a couple whose moment is equal to”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Zero at its upper end is the correct answer to “A ladder is resting on a rough ground and leaning against a smooth vertical wall. The force of friction will act”. This question is standard in competitive examination syllabi for Engineering Mechanics.

Upward at its upper end is the correct answer to “A ladder is resting on a smooth ground and leaning against a rough vertical wall. The force of friction will act”. This question is standard in competitive examination syllabi for Engineering Mechanics.

16 cm4 is the correct answer to “The moment of inertia of a rectangular section 3 cm wide and 4 cm deep about X-X axis is”. This question is standard in competitive examination syllabi for Engineering Mechanics.