A uniform rod AB of length L = 1 m is sliding along two mutually perpendicular surfaces OP and OQ as shown in the figure.

When the rod subtends an angle $$\theta$$ = 30$$^\circ$$ with OQ, the end B has a velocity $$\sqrt3$$ m/s. The velocity of end A at that time is

A block of mass 10 kg rests on a rough inclined plane making an angle of 30$$^\circ$$ with the horizontal. The coefficient of static friction between the block and the plane is 0.1. The friction force on the block is

When a body is dropped from a height h, then it hits the ground with a momentum p. If the same body is dropped from a height which is three times more than previous height, the percentage change in momentum when it hits the ground is

A plane requires for take off a speed of 72 kmh^$$-$$1, the run on the ground being 50 m. The mass of the plane is 10000 kg and the coefficient of friction between the plane and the ground is 0.2. Assume that the plane accelerates uniformly during take off. The minimum force required by the engine of the plane for take off is