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Q.

Figure represents a light inextensible string ABCDE in which AB = BC = CD = DE and to which are attached masses M, m, and M at the points B, C, and D, respectively. The system hangs freely in equilibrium with ends A and E of the string fixed in the same horizontal line. It is given that tan α = 3/4 and tan β = 12/5. Then the tension in thestring BC is

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a

2 mg

b

(13/10) mg

c

(3/10) mg

d

(20/11) mg

answer is B.

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Detailed Solution

tan⁡β=125 ∴cos⁡β=513T1cos⁡β+T2cos⁡β=mg    ......(i)T1sin⁡β=T2sin⁡β    ......(ii)∴ T1=T2=T∴ 2Tcos⁡β=mg ⇒T=mg2cos⁡β⇒T=1310mg
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Figure represents a light inextensible string ABCDE in which AB = BC = CD = DE and to which are attached masses M, m, and M at the points B, C, and D, respectively. The system hangs freely in equilibrium with ends A and E of the string fixed in the same horizontal line. It is given that tan α = 3/4 and tan β = 12/5. Then the tension in thestring BC is