Question 303: Work, Energy and Power & Circular Motion

Question

A mass is whirled in a circular path with constant angular velocity and its linear velocity is $v$. If the string is now halved keeping the angular momentum same, the linear velocity is

Accepted Answer

Angular velocity $=\omega$
Linear velocity $=v$
Length of string = Radius $=r$
If string is halved, $r^{\prime}=\frac{r}{2}$
Angular momentum, $L=\mathbf{r} 	imes \mathbf{p}$
where, $\mathbf{r}=$ radius vector and $\mathbf{p}=$ linear momentum.
$$\begin{array}{ll}
=r 	imes m v & {[\because 	heta=90^\circ}] \
=m v r &
\end{array}$$
As $L$ remain constant,
$$m v r=	ext { constant }$$
$\Rightarrow$ If $r^{\prime} ightarrow \frac{r}{2}, v^{\prime}=2 v$ such that
$$\begin{aligned}
m v^{\prime} r^{\prime} & =m 2 v 	imes \frac{r}{2} \
& =m v r
\end{aligned}$$
Hence, linear velocity will be $2 v$.

Answer

$2 v$

Answer

$\frac{v}{2}$

Answer

$v$

Answer

$v \sqrt{2}$

Work, Energy and Power & Circular Motion

A mass is whirled in a circular path with constant angular velocity and its linear velocity is v. If the string is now halved keeping the angular momentum same, the linear velocity is

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