Question

A particle crossed the topmost point C of a vertical circle with critical speed; then the ratio of velocities at points A, B and C is –

• A. 3: 2 : 1
• B. 5 : 3 : 1
• C. 5² : 3² : 1²
• D. $\sqrt{5}$ : $\sqrt{3}$ : $\sqrt{1}$

Answer 1

Answer: (D)

$\sqrt{5}$ : $\sqrt{3}$ : $\sqrt{1}$

Answer 2

\ K + U = mgH & K = 2U

\ 2U + U = mgH

̃ U = $\frac{mgH}{3}$ ̃ mgh =

$\frac{mgH}{3}$ ̃ h = H/3

\ $\frac{1}{2}$ mv² = 2U = $\frac{2mgH}{3}$ ̃ v = $2\sqrt{\frac{gH}{3}}$