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

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

Bissoy MCQ
#Mechanical Engineering #Engineering Mechanics

Related Questions

If a number of forces are acting at a point, their resultant will be inclined at an angle $$\theta $$ with the horizontal, such that
A $$\tan \theta = \frac{{\sum {\text{H}} }}{{\sum {\text{V}} }}$$
B $$\tan \theta = \frac{{\sum {\text{V}} }}{{\sum {\text{H}} }}$$
C $$\tan \theta = \sum {{\text{V}} \times \sum {\text{H}} } $$
D $$\tan \theta = \sqrt {\sum {{\text{V}} + \sum {\text{H}} } } $$
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
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 $$2{\text{P}}\cot \frac{\theta }{2}$$
If the resultant of two forces has the same magnitude as either of the force, then the angle between the two forces is
A 30°
B 45°
C 60°
D 120°
The resultant of two forces P and Q is R. If Q is doubled, the new resultant is perpendicular to P. Then,
A P = R
B Q = R
C P = Q
D None of the above is correct
The resultant of the two forces ‘P’ and ‘Q’ is ‘R’. If ‘Q’ is doubled, the new resultant is perpendicular to ‘P’. Then
A P = Q
B Q = R
C Q = 2R
D None of these
The resultant of the two forces P & Q is R. If Q is doubled, the new resultant is perpendicular to P. Then
A P = Q
B Q = R
C Q = 2R
D Q = 3R

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