The centripetal acceleration is given by

A particle is moving on a circular path with constant speed, then its acceleration will be

A particle is moving with uniform speed along the circumference of a circle of radius $R$ under the action of a central fictitious force $F$ which is inversely proportional to $R ^{3}$. Its time period of revolution will be given by

A wheel is of diameter $1\ m.$ If it makes $30$ revolution per second, then the linear speed of a point on its circumference will be 

For circular motion, if ${\vec a_t},\,{\vec a_c},\,\vec r$ and $\vec v$ are tangential acceleration, centripetal acceleration, radius vector and velocitym respectively, then find the wrong relation

A boy ties a stone of mass $100 \,g$ to the end of a $2$ $m$ long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of $80 \,N$. If the maximum speed with which the stone can revolve is $\frac{ K }{\pi} rev$. / $min$. The value of $K$ is (Assume the string is massless and unstretchable)