A child starts running from rest along a circular track of radius $r$ with constant tangential acceleration a. After time $t$ he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is
[g = acceleration due to gravity]
A body is moving along a circular track of radius 100 m with velocity $20 \mathrm{~m} / \mathrm{s}$. Its tangential acceleration is $3 \mathrm{~m} / \mathrm{s}^2$, then its resultant acceleration will be
A particle starting from rest moves along the circumference of a circle of radius $$r$$ with angular acceleration $$\alpha$$. The magnitude of the average velocity, in the time it completes the small angular displacement $$\theta$$ is
A particle of mass $$m$$ is performing UCM along a circle of radius $$r$$. The relation between centripetal acceleration $$a$$ and kinetic energy $$E$$ is given by