A particle moves around a circular path of radius '$$r$$' with uniform speed '$$V$$'. After moving half the circle, the average acceleration of the particle is

On dry road, the maximum speed of a vehicle along a circular path is '$$V$$'. When the road becomes wet, maximum speed becomes $$\frac{\mathrm{V}}{2}$$. If coefficient of friction of dry road is '$$\mu$$' then that of wet road is

A string of length '$$L$$' fixed at one end carries a body of mass '$$\mathrm{m}$$' at the other end. The mass is revolved in a circle in the horizontal plane about a vertical axis passing through the fixed end of the string. The string makes angle '$$\theta$$' with the vertical. The angular frequency of the body is '$$\omega$$'. The tension in the string is

A stone is projected at angle $$\theta$$ with velocity $$u$$. If it executes nearly a circular motion at its maximum point for short time, then the radius of the circular path will be ( $$g=$$ acceleration due to gravity)