The force required to move the body up the plane will be minimum if it makes an angle with the inclined plane __________ the angle of friction.

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

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