When helical gear $M$ turns as shown,gears $I$ & $H$ turn in the following manner. Which of the following is correct? (Assuming no slipping anywhere)

$A$ child of mass $5\,kg$ is going round a merry-go-round that makes $1$ rotation in $3.14\,s$. The radius of the merry-go-round is $2\,m$. The centrifugal force on the child will be $.......\,N$.

$A$ body of mass $m$ is moving with speed $V$ along a circular path of radius $r$. Now,the speed is reduced to $\frac{V}{2}$ and the radius is increased to $3r$. For this change,the initial centripetal force needs to be:

$A$ particle of mass $m$ is rotating in a plane in a circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on the particle is

$A$ particle of mass $m$ is fixed to one end of a light spring having force constant $k$ and unstretched length $\ell$. The other end is fixed. The system is given an angular speed $\omega$ about the fixed end of the spring such that it rotates in a circle in gravity-free space. Then the stretch in the spring is

$A$ particle of mass $m$ is suspended from a ceiling through a string of length $L$. The particle moves in a horizontal circle of radius $r$ such that $r = \frac{L}{\sqrt{2}}$. The speed of the particle will be: