If a number of forces are acting at a point, their resultant will be inclined at an angle $$\theta $$ with the horizontal, such that

The resultant of two forces P and Q acting at an angle $$\theta $$ is

A

$$\sqrt {{{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{PQ}}\sin \theta } $$

B

$$\sqrt {{{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{PQ}}\cos \theta } $$

C

$$\sqrt {{{\text{P}}^2} + {{\text{Q}}^2} - 2{\text{PQ}}\cos \theta } $$

D

$$\sqrt {{{\text{P}}^2} + {{\text{Q}}^2} - 2{\text{PQ}}\tan \theta } $$

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

A

sinθ

B

cosθ

C

tanθ

D

cosecθ

A semicircular disc rests on a horizontal surface with its top flat surface horizontal and circular portion touching down. The coefficient of friction between semi circular disc and horizontal surface is µ. This disc is to be pulled by a horizontal force applied at one edge and it always remains horizontal. When the disc is about to start moving, its top horizontal force will

A

Remain horizontal

B

Slant up towards direction of pull

C

Slant down towards direction of pull

D

None of the above

Two forces of magnitude 3m and 2m respectively have a resultant R. if the first force is doubled, the magnitude of the resultant is doubled.Find the angle betuween forces?

A

90°

B

120°

C

135°

D

145°

3N ও 2N মানের দুইটি বলের লদ্ধি R । প্রথম বলের মান দ্বিগুণ করলে লদ্ধির মানও দ্বিগুণ হয়। বলদ্বয়ের মধ্যবর্তী কোণের মান হবে- (The resultant of two forces 3N and 2N is R. If the first force is doubled then the resultant is also doubled. The angle between the forces is-)

A

30°

B

45°

C

65°

D

120°

If the resultant of two equal forces has the same magnitude as either of the forces, then the angle between the two forces is

A

30°

B

60°

C

90°

D

120°

Parallelogram Law of Forces states, "if two forces acting simultaneously on a particle be represented in magnitude and direction by two adjacent sides of a parallelogram, their resultant may be represented in magnitude and direction by

A

Its longer side

B

Its shorter side

C

The diagonal of the parallelogram which does not pass through the point of intersection of the forces

D

The diagonal of the parallelogram which passes through the point of intersection of the forces

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

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

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

$$2{\text{P}}\cot \frac{\theta }{2}$$

The resolved part of the resultant of two forces inclined at an angle 'θ' in a given direction is equal to

A

The algebraic sum of the resolved parts of the forces in the given direction

B

The sum of the resolved parts of the forces in the given direction

C

The difference of the forces multiplied by the cosine of θ

D

The sum of the forces multiplied by the sine of θ

If a number of forces are acting at a point, their resultant will be inclined at an angle $$\theta $$ with the horizontal, such that

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