A lift of mass $100$ kg starts moving from rests in the upward direction. Fig shows the variation if speed of the lift, $T_{1}, T_{2}$ and $T_{3}$ stand for tension in the rope form zero to two seconds, two to six seconds, six to seven seconds respectively then:-

T_{1} : T_{2} : T_{3} :: 1 : 1 : 1

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T_{1} : T_{2} : T_{3} :: 6 : 5 : 3

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T_{1} : T_{2} : T_{3} :: 3 : 5 : 6

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T_{1} : T_{2} : T_{3} :: 6 : 5 : 6

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Solution

The correct option is B $T_{1} : T_{2} : T_{3} :: 6 : 5 : 3$
$\begin{matrix} F o r e a c h i n t e r v a l o f t i m e, t h e s l o p e i s : 2, 0 a n d - 4 r e s p e c t i v e l y . A n d t h e e q u a t i o n o f m o t i o n i s; T = m (g + a) \Rightarrow 100 \times (g + a) F o r f i r s t i n t e r v a l o f t i m e w e h a v e a = 2 m / s^{2} h e n c e, T_{1} = 100 \times 12 = 1200 N T_{2} = 100 \times g = 100 \times 10 = 1000 N T_{3} = 100 \times (g - 4) = 100 \times (10 - 4) = 100 (6) = 600 N r a t i o o f t h e t e n s i o n s a r e - 6 : 5 : 3 \end{matrix}$
Hence,
option $(B)$ is correct answer.

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