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. $$\frac{{\text{P}}}{{\sin \alpha }} = \frac{{\text{Q}}}{{\sin \gamma }} = \frac{{\text{R}}}{{\sin \beta }}$$
Answer: Option B
This Question Belongs to Mechanical Engineering >> Engineering Mechanics
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. $$2{\text{P}}\cot \frac{\theta }{2}$$
A. Equal to
B. Less than
C. Greater than
D. None of these
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. $$\sqrt {{{\left( {\sum {\text{V}} } \right)}^2} + {{\left( {\sum {\text{H}} } \right)}^2} + 2\left( {\sum {\text{V}} } \right)\left( {\sum {\text{H}} } \right)} $$
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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