Question

Mass of 2 kg is moving with a string in horizontal circle with angular velocity 5 cycle/m 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

The correct option is D 7 cycles/min

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

$v\propto \sqrt{T}$

$\frac{v_1}{v_2}=(\frac{T_1}{T_2}{)}^{1/2}=(\frac{2T_2}{T_2}{)}^{1/2}$

$v_2=\sqrt{2}{v}_1=\sqrt{2}\times 5$

$=5\times 14=7$ cycles/min.