Two spheres of equal masses are attached to a string of length 2m as shown. The string and the spheres are then whirled in a horizontal circle about O at a constant rate. If T1 is the tension in the string between P & Q and T2 is the tension in the string between P & O then T1/ T2 equals to (P is connected to the mid point of string)

T1=m(2)ω2 T2−T1=m(1)ω2 ⇒T2=mω2+T1=mω2+2mω2=3mω2 ∴T1T2=23

Two spheres of equal masses are attached to a string of length 2m as shown. The string and the spheres are then whirled in a horizontal circle about O at a constant rate. If T1 is the tension in the string between P & Q and T2 is the tension in the string between P & O then T1/ T2 equals to (P is connected to the mid point of string)

T1=m(2)ω2 T2−T1=m(1)ω2 ⇒T2=mω2+T1=mω2+2mω2=3mω2 ∴T1T2=23

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Two spheres of equal masses are attached to a string of length 2m as shown. The string and the spheres are then whirled in a horizontal circle about O at a constant rate. If T₁ is the tension in the string between P & Q and T₂ is the tension in the string between P & O then T₁/ T₂ equals to (P is connected to the mid point of string)

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$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{3}$

answer is C.

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Detailed Solution

$T_{1} = m (2) ω^{2} T_{2} - T_{1} = m (1) ω^{2} \Rightarrow T_{2} = m ω^{2} + T_{1} = m ω^{2} + 2 m ω^{2} = 3 m ω^{2} ∴ \frac{T_{1}}{T_{2}} = \frac{2}{3}$

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