First slide

Force

Question

The whole set up shown in the figure where particles ( m₁ and m₂ are) rotating with constant angular velocity w on a horizontal frictionless table. If T₁ and T₂ are tension in given strings then ratio of tensions T₁/T₂ is:

Moderate

A

M₁/M₂
B

$M_{1} + 2 M_{2} / 2 M_{2}$
C

$M_{2} / M_{1}$
D

$M_{2} + M_{1} / M_{1}$

Solution

$T_{1} = m_{1} ω^{2} ℓ_{1} + m_{2} ω^{2} ℓ_{2}$
$T_{2} = m_{2} ω^{2} ℓ_{2}$
$\frac{T_{1}}{T_{2}} = \frac{m_{1} ℓ_{1} + m_{2} ℓ_{2}}{m_{2} ℓ_{2}} = \frac{m_{1} + 2 m_{2}}{2 m_{2}}$

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