Question

What minimum horizontal speed should be given to a particle of mass $m$ attached to a rigid rod of length $10\text{m}$ so that it describes a complete vertical circular motion?

• A. $22.36\text{m/s}$
• B. $10\text{m/s}$
• C. $20\text{m/s}$
• D. depend upon the mass of particle

Answer 1

The correct option is C $20\text{m/s}$

Since the rod is rigid, the particle can reach the topmost point with zero velocity to describe a complete circular motion.


Now using energy conservation between $A$ and $B$, taking $A$ as a reference
$K_A+U_A=U_B+K_B$
$\frac{1}{2}m{v}^2+0=mg\left(20\right)+0$
$\Rightarrow v^2=2g\left(20\right)$
$\Rightarrow v^2=40g=400$
$\Rightarrow v=\sqrt{400}=20\text{m/s}$ is the minimum velocity that must be given to the particle.