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 the
string BC is

Question

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 the
string BC is

Infinity Learn · Accepted Answer

$$tan$$⁡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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