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Complex Numbers And Quadratic Equations

Question
CBSEENMA11015585

A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are 

  • 12 kg and 13 kg

  • 5 kg and 5 kg

  • 5 kg and 12 kg

  • 5 kg and 13 kg

Solution

C.

5 kg and 12 kg


straight T subscript 2 space cos space open parentheses straight pi over 2 minus straight theta close parentheses space equals space straight T subscript 1 space cosθ
rightwards double arrow space straight T subscript 1 space cos space straight theta space equals space straight T subscript 2 space sin space straight theta
straight T subscript 1 space sin space straight theta space plus space straight T subscript 2 space cos space straight theta space equals space 13
because space OC space equals space CA space space equals CB
rightwards double arrow space angle space AOC space equals space angle OAC space and space angle COB space equals space angle OBC
therefore space sin space straight theta space equals space sin space straight A space equals space 5 over 13 space and space cos space straight theta space equals 12 over 13
rightwards double arrow space straight T subscript 1 over straight T subscript 2 space equals space 5 over 12 space rightwards double arrow space straight T subscript 1 space equals space 5 over 12 space and space cos space straight theta space equals space 12 over 13
rightwards double arrow space straight T subscript 1 over straight T subscript 2 space equals space 5 over 12 space rightwards double arrow space straight T subscript 1 space equals space 5 over 12 straight T subscript 2
straight T subscript 2 space open parentheses 5 over 12.5 over 13.12 over 13 close parentheses space equals space 13
straight T subscript 2 space open parentheses fraction numerator 169 over denominator 12.13 end fraction close parentheses space equals space 13
straight T subscript 2 space equals space 12 space kgs
rightwards double arrow space straight T subscript 1 space equals space 5 space kgs