The resultant of the following three couples 20 kg force, 0.5 m arm, +ve sense 30 kg force, 1 m arm, -ve sense 40 kg force, 0.25 m arm, +ve sense having arm of 0.5 m will be

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 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

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 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