Question

A person throws a stick of length $2\text{m}$ such that the centre of the stick is moving vertically upwards with a velocity $5\text{m/s}$ and the angular velocity of the stick about its centre is $10\text{rad/s}$. Find the magnitude of velocity of end $A$ of the rod when $\text{COM}$ of the rod reaches maximum height.

• A. zero
• B. $5\text{m/s}$
• C. $10\text{m/s}$
• D. $15\text{m/s}$

Answer 1

The correct option is C $10\text{m/s}$

At maximum height, the vertical component of velocity of $\text{COM}$ will be zero.
i.e ${\overrightarrow{V}}_O=0...\left(i\right)$
Length of rod, $L=2\text{m}$
Hence, velocity of end $A$ at maximum height,
${\overrightarrow{V}}_A={\overrightarrow{V}}_O+{\overrightarrow{V}}_{AO}...\left(ii\right)$
$|{\overrightarrow{V}}_{AO}|=r\omega =\frac{L}{2}\times \omega =1\times 10=10\text{m/s}$
From Eq $\left(i\right)\&\left(ii\right)$,
${\overrightarrow{V}}_A={\overrightarrow{V}}_{AO}$
$\Rightarrow |{\overrightarrow{V}}_A|=|{\overrightarrow{V}}_{AO}|$
$\therefore |{\overrightarrow{V}}_A|=10\text{m/s}$