Question

$ABCD$ is smooth horizontal fixed plane on which mass $m_1=0.1kg$is moving in a circular path of radius $1m$. It is connected by an idea string which is passing through a smooth hole and connects mass $m_2=\frac{1}{\sqrt{2}}kg$ at the other end as shown. $m_2$ also moves in a horizontal circle of same radius of $1m$ with a speed of $\sqrt{10}m/s$. If $g=10m/s^2$, then the speed of $m_1$ is:

• A. $\sqrt{10}m/s$
• B. $10m/s$
• C. $1/\sqrt{10}m/s$
• D. none of these

Answer 1

The correct option is B $10m/s$

$m_1=0.1kg$

$r_{m_1}=1m$

$m_2=\frac{1}{\sqrt{2}}kg$

$r_{m_2}=1m$

$v=\sqrt{10}m/s$

Since string is mass less tension on string will be same.

$T\cos \theta =mg=\frac{g}{\sqrt{2}}$

$T\sin \theta =\frac{m_2{v}^2}{R}=\frac{10}{\sqrt{2}}$

$T=\sqrt{(\frac{g}{\sqrt{2}}{)}^2+(\frac{10}{\sqrt{2}}{)}^2}$

$=\sqrt{\frac{200}{2}}$

$=10N$

$10=\frac{m_1{v}^2}{R}=\frac{0.1}{1}{v}^2$

$v^2=100,v=10m/s$