If a number of coplanar forces acting at a point be in equilibrium, the sum of clockwise moments must be __________ the sum of anticlockwise moments, about any point.

Varingon's theorem of moments states that if a number of coplanar forces acting on a particle are in equilibrium, then

A

Their algebraic sum is zero

B

Their lines of action are at equal distances

C

The algebraic sum of their moments about any point in their plane is zero

D

The algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point

According to the law of moments, if a number of coplanar forces acting on a particle are in equilibrium, then

A

Their algebraic sum is zero

B

Their lines of action are at equal distances

C

The algebraic sum of their moments about any point in their plane is zero

D

The algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point

The below figure shows the three coplanar forces P, Q and R acting at a point O. If these forces are in equilibrium, then

A

$$\frac{{\text{P}}}{{\sin \beta }} = \frac{{\text{Q}}}{{\sin \alpha }} = \frac{{\text{R}}}{{\sin \gamma }}$$

B

$$\frac{{\text{P}}}{{\sin \alpha }} = \frac{{\text{Q}}}{{\sin \beta }} = \frac{{\text{R}}}{{\sin \gamma }}$$

C

$$\frac{{\text{P}}}{{\sin \gamma }} = \frac{{\text{Q}}}{{\sin \alpha }} = \frac{{\text{R}}}{{\sin \beta }}$$

D

$$\frac{{\text{P}}}{{\sin \alpha }} = \frac{{\text{Q}}}{{\sin \gamma }} = \frac{{\text{R}}}{{\sin \beta }}$$

The below figure shows the three coplanar forces P, Q and R acting at a point O. If these forces are in equilibrium, then
Engineering Mechanics mcq question image

Engineering Mechanics mcq question image

A

$$\frac{{\text{P}}}{{\sin \beta }} = \frac{{\text{Q}}}{{\sin \alpha }} = \frac{{\text{R}}}{{\sin \gamma }}$$

B

$$\frac{{\text{P}}}{{\sin \alpha }} = \frac{{\text{Q}}}{{\sin \beta }} = \frac{{\text{R}}}{{\sin \gamma }}$$

C

$$\frac{{\text{P}}}{{\sin \gamma }} = \frac{{\text{Q}}}{{\sin \alpha }} = \frac{{\text{R}}}{{\sin \beta }}$$

D

$$\frac{{\text{P}}}{{\sin \alpha }} = \frac{{\text{Q}}}{{\sin \gamma }} = \frac{{\text{R}}}{{\sin \beta }}$$

A college council is auditioning students for a cultural festival. They must satisfy the following criteria — 1. Student must know at least one dance form. 2. Student must know to play at least one musical instrument. 3. Student must have good acting skills. Which one of the following will the council definitely select? A. Z is a Bharat Natyam dancer, a violinist but does not have any acting skills. B. P plays football, guitar, has acted in road shows and is a classical dancer. C. J is a contemporary dancer, a great actor and is planning to learn flute. D. A plays sitar, is a hip-hop dancer and does not have any acting skills.

A

B

C

A

D

A college council is auditioning students for a cultural festival. They must satisfy the following criteria – I. Student must know at least one dance form. II. Student must know to play at least one musical instrument. III. Student must have good acting skills. Which one of the following will the council definitely select? A. Z is a Bharat Natyam dancer, a violinist but does not have any acting skills. B. P plays football, guitar, has acted in road shows and is a classical dancer. C. J is a contemporary dancer, a great actor and is planning to learn flute. D. A plays sitar is a hip - hop dancer and does not have any acting skills.

A

B

C

D

How far is point 'R' from Point 'T'? Statement (I): Point 'R' is 5 metres to the north of point 'M'. Point 'U' is 4 metres to the east of point 'R'. Point 'T' is to the west of point 'R' such that points 'U' 'R' and 'T' form a straight line of metres. Statement (II): Point 'Z' is metres to the south of point 'T'. Point 'U' is metres to the east of point 'T'. Point 'M' is metres to the east of point 'Z'. Point 'R' is metres to the north of point 'M'. Point 'R' lies on the line formed by joining points 'T' and 'U'.

A

Statement (I) and (III) are independently sufficient to answer the question.

B

Statement (I) and (II) are together required to answer the question.

C

Statement (I) alone is sufficient to answer the question while statement (II) is not sufficient to answer the question.

D

Statement (II) alone is sufficient to answer (I) is not sufficient to answer the question.

Point A is 3m in the north of point B. Point D is 2m in the east of point E. Point F is 9m in the west of point G. Point C is 4m in the west of point B. Point C is 3m in the south of point D. Point F is 5m in the south of point E. Point H is 5m in the north of point G. What is the shortest distance between point H and point A?

A

5m

B

4m

C

3m

D

6m

The system of forces acting on the aircraft are propulsive forces, aerodynamic forces, gravitational forces and these result in inertial forces.

A

True

B

False

Point P is 4m in the west of point V. Point R is 6m in the north of point Q. Point T is 5m in the south of point S. Point V is in the middle of point R and Q. Point U is 5m in the east of point R. Point V is in north of point Q. Point S is 5m in the east of point V. What is the area of triangle formed by point P, R and Q?

A

14m²

B

15m²

C

16m²

D

12m²

If a number of coplanar forces acting at a point be in equilibrium, the sum of clockwise moments must be __________ the sum of anticlockwise moments, about any point.

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