Newtons 2nd Law applied to Particles in Circular Motion

Q. A particle of mass $m$ is suspended from a ceilling through a string of length $L$ the particle moves in a horizontal circle of radius r. what is the speed of the particle and the tension in the string for conical pendulum ?

1. $\upsilon =\frac{r\sqrt{grl}}{(L^2-r^2{)}^{1/4}},T=\frac{mgL}{\sqrt{L^2-r^2}}$
2. $\upsilon =\frac{r\sqrt{g}}{(L^2-r^2{)}^{1/4}},T=\frac{mgL}{\sqrt{L^2-r^2}}$
3. $\upsilon =\frac{r\sqrt{g}}{(L^2-r^2{)}^{1/4}},T=\frac{mgL}{r}$
4. $\upsilon =\frac{\sqrt{grL}}{(L^2-r^2{)}^{1/4}},T=\frac{mgr}{\sqrt{L^2-r^2}}$

Q. A particle of mass $2kg$ is travelling at a velocity of $1.5m/s$. A force $t\left(t\right)=3t^2$ (in N) is applied to it in the direction of motion for a duration of $2$ seconds. Where $t$ denotes time in seconds. The velocity (in $m/s$ up to one decimal place) of the particle immediately after the removal of the force is

1. 5.5

Q. A chain of length l and mass m lies on the surface of a smooth sphere of radius R (R > l) with one end tied to the top of the sphere. The tangential acceleration of the chain when the chain starts sliding down is.

1. $\frac{2Rg}{l}[2-cos\frac{l}{R}]$
2. $\frac{Rg}{l}[2-cos\frac{l}{R}]$
3. $\frac{Rg}{l}[1-cos\frac{l}{R}]$
4. $\frac{Rg}{2l}[1-cos\frac{l}{R}]$