Question

A particle is moving along a vertical circular path of radius $r$. When the circular path is just completed:

• A. the velocity at highest position is $\sqrt{rg}$
• B. the velocity at highest position is zero
• C. the velocity at lowest position is $\sqrt{5rg}$
• D. the tension in string at the lowest position is $6mg$

Answer 1

Answer: (A), (C), (D)

The correct options are
A the velocity at highest position is $\sqrt{rg}$
C the tension in string at the lowest position is $6mg$
D the velocity at lowest position is $\sqrt{5rg}$

Considering the upper most point as 1 and the lowest point as 2 , also consider $V_t$ and $V_b$ as velocity at top most and bottom most point,
$T_1+mg=\frac{m{V}_t^2}{R}$
$T_1=0$ at highest point
$V_t=\sqrt{gR}$

$\frac{1}{2}m{V}_b^2-\frac{1}{2}m{V}_t{}^2=2mgR$

$V_b=\sqrt{5Rg}\left(atlowestpoint\right)$

$T_2-mg=\frac{m{V}_b^2}{R}\left(atlowestpoint\right)$

$T_2=mg+\frac{m{V}_b^2}{R}$
$T=6mg$