Engineering Mechanics MCQ Questions & Answers

1

The resultant of two equal forces P making an angle $$\theta ,$$ is given by

A) $$2{\text{P}}\sin \frac{\theta }{2}$$ B) $$2{\text{P}}\cos \frac{\theta }{2}$$ C) $$2{\text{P}}\tan \frac{\theta }{2}$$ D) $$2{\text{P}}\cot \frac{\theta }{2}$$

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Answer & Solution

Answer: Option B

Solution:

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.

2

A framed structure is perfect, if the number of members are __________ (2j - 3), where j is the number of joints.

A) Equal to B) Less than C) Greater than D) None of these

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Answer & Solution

Answer: Option A

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3

If a number of forces are acting at a point, their resultant is given by

A) $${\left( {\sum {\text{V}} } \right)^2} + {\left( {\sum {\text{H}} } \right)^2}$$ B) $$\sqrt {{{\left( {\sum {\text{V}} } \right)}^2} + {{\left( {\sum {\text{H}} } \right)}^2}} $$ C) $${\left( {\sum {\text{V}} } \right)^2} + {\left( {\sum {\text{H}} } \right)^2} + 2\left( {\sum {\text{V}} } \right)\left( {\sum {\text{H}} } \right)$$ D) $$\sqrt {{{\left( {\sum {\text{V}} } \right)}^2} + {{\left( {\sum {\text{H}} } \right)}^2} + 2\left( {\sum {\text{V}} } \right)\left( {\sum {\text{H}} } \right)} $$

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Answer & Solution

Answer: Option B

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4

The linear acceleration (a) of a body rotating along a circular path of radius (r) with an angular acceleration of $$\alpha $$ rad/s², is

A) $${\text{a}} = \frac{\alpha }{{\text{r}}}$$ B) $${\text{a}} = \alpha {\text{r}}$$ C) $${\text{a}} = \frac{{\text{r}}}{\alpha }$$ D) None of these

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Answer & Solution

Answer: Option B

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5

Moment of inertia of a circular section about an axis perpendicular to the section is

A) $$\frac{{\pi {{\text{d}}^3}}}{{16}}$$ B) $$\frac{{\pi {{\text{d}}^3}}}{{32}}$$ C) $$\frac{{\pi {{\text{d}}^4}}}{{32}}$$ D) $$\frac{{\pi {{\text{d}}^4}}}{{64}}$$

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Answer & Solution

Answer: Option C

Solution:

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.

6

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.)

A) $${I_{\text{P}}} = {I_{\text{G}}} + {\text{A}}{{\text{h}}^2}$$ B) $${I_{\text{P}}} = {I_{\text{G}}} - {\text{A}}{{\text{h}}^2}$$ C) $${I_{\text{P}}} = \frac{{{I_{\text{G}}}}}{{{\text{A}}{{\text{h}}^2}}}$$ D) $${I_{\text{P}}} = \frac{{{\text{A}}{{\text{h}}^2}}}{{{I_{\text{G}}}}}$$

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Answer & Solution

Answer: Option A

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7

The friction experienced by a body, when at rest, is known as

A) Static friction B) Dynamic friction C) Limiting friction D) Coefficient of friction

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Answer & Solution

Answer: Option A

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8

The energy possessed by a body, for doing work by virtue of its position, is called

A) Potential energy B) Kinetic energy C) Electrical energy D) Chemical energy

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Answer & Solution

Answer: Option A

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9

The coefficient of friction depends upon

A) Nature of surfaces B) Area of contact C) Shape of the surfaces D) All of the above

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Answer & Solution

Answer: Option A

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10

For any system of coplanar forces, the condition of equilibrium is that the

A) Algebraic sum of the horizontal components of all the forces should be zero B) Algebraic sum of the vertical components of all the forces should be zero C) Algebraic sum of moments of all the forces about any point should be zero D) All of the above

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Answer & Solution

Answer: Option D

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Engineering Mechanics MCQ Questions & Answers | Mechanical Engineering