Question

Mass of $2kg$ is moving with a string in horizontal circle with angular velocity $5$ cycles/min keeping the radius constant, tension in string is doubled. Now, the angular velocity of the mass will be

• A. 14 cycles/min
• B. 10 cycles/min
• C. 2.25 cycles/min
• D. 7 cycles/min

Answer 1

Answer: (D)

Tension in the string should be equal to centripetal force
$T=\frac{m{v}^2}{r}$
where, $m=$ mass of body
$r=$ radius of circular path
$v=$ linear velocity of body
$m$ and $r$ are constant.
Hence, $v\propto \sqrt{T}$
$\therefore \frac{v_2}{v_1}={\left(\frac{T_2}{T_1}\right)}^{1/2}={\left(\frac{2T_1}{T_1}\right)}^{1/2}$
$v_2=\sqrt{2}{v}_1=\sqrt{2}\times 5$
$=5\times 1.4=7$ cycles/min