A rectangular frame is to be suspended symmetrically by two strings of equal length on two supports (Fig. 9.2). It can be done in one of the following three ways The tension in the strings will be

(a) The same in all cases

(b) Least in (a)

(c) Least in (b)

(d) Least in (c)

This is a multiple choice answer as classified in NCERT Exemplar

(c) 2Tsin $\theta$ -mg=0

2Tsin $\theta$ =mg

Total horizontal forces = Tcos $\theta -Tcos\theta =0$

T=mg/2sin $\theta$

As mg is constant T $\propto \frac{1}{sin\theta }$

T_max= mg/sin $\theta$ _min

Sin $\theta$ _min=0, $\theta$ _min= 0

T_min=mg/2sin $\theta$ _max

_{$sin\theta$ max}= 1, $\theta$ =90⁰

<p><span data-teams="true">This is a multiple choice answer as classified in NCERT Exemplar</span></p><p> (c) 2Tsin<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>-mg=0</p><p>2Tsin<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>=mg</p><p>Total horizontal forces = Tcos<span contenteditable="false"> <math> <mi>θ</mi> <mo>-</mo> <mi>T</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </math> </span></p><p>T=mg/2sin<span contenteditable="false"> <math> <mi>θ</mi> </math> </span></p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745486685phptvNxA5_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745486685phptvNxA5.jpeg" alt="" width="252" height="198"></picture></div><div><p>As mg is constant T<span contenteditable="false"> <math> <mo>∝</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>θ</mi> </mrow> </mrow> </mfrac> <mi> </mi> </math> </span></p><p>T_max= mg/sin<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>_min</p><p>Sin<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>_min=0, <span contenteditable="false"> <math> <mi>θ</mi> </math> </span>_min= 0</p><p>T_min=mg/2sin<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>_max</p><p>_{<span contenteditable="false"> <math> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>θ</mi> </math> </span>max}= 1, <span contenteditable="false"> <math> <mi>θ</mi> </math> </span>=90⁰</p></div></div>

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