Two weights of the mass m₁ and m₂ (> m₁) are joined by an inextensible string of negligible mass passing over a fixed frictionless pulley. The magnitude of the acceleration of the loads is

A block of mass m₂ is placed on a horizontal table and another block of mass m₁ is placed on top of it. An increasing horizontal force F = at is exerted on the upper block but the lower block never moves as a result. If the coefficient of friction between the blocks is $$\mu$$₁ and that between the lower block and the table is $$\mu$$₂, then what is the maximum possible value of $$\mu$$₁ / $$\mu$$₂ ?

The velocity (v) of a particle (under a force F) depends on its distance (x) from the origin (with x > 0) $$v \propto {1 \over {\sqrt x }}$$. Find how the magnitude of the force (F) on the particle depends on x?

A block of mass 1 kg starts from rest at x = 0 and moves along the X-axis under the action of a force F = kt, where t is time and k = 1 Ns^$$-$$1. The distance the block will travel in 6 seconds is