Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle $$\theta $$ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle $$\theta $$ is -

A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point. the rope deviated at an angle of 45^o at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (g = 10 ms^$$-$$2

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (take g = 10 ms^$$-$$2)

Two masses m₁ = 5 kg and m₂ = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m₂ to stop the motion is :