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The entries in Column – II show some arrangements of two or more blocks connected by means of light inextensible ropes and smooth pulley. The tension in the string PQ is $T = ηmg$ . Column – I lists some value of $η$ . Match appropriate options (neglect friction)
Column - I
Column - II
A. $η = \frac{1}{2}$ P.

B. $η = \frac{4}{3}$ Q.

C. $η = \frac{8}{3}$ R.

D. $η = \frac{2}{3}$ S.

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$A - Q, B - P, C - RS, D - S$

$A - S, B - Q, C - R, D - P$

$A - R, B - S, C - P, D - Q$

$A - P, B - R, C - S, D - Q$

answer is A.

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Detailed Solution

For p

$a = \frac{m g}{2 m} = \frac{g}{2}$

$m g - T = m a$

$T = \frac{m g}{2}$

$F o r a a \frac{m g}{3 m} = \frac{g}{m}$

$m g - T_{2} = \frac{m g}{3}$

$T_{2} = \frac{2 m g}{3}$

For R a = g/3

$m g - T = \frac{m g}{3}$

$T = \frac{2 m g}{3}$

$2 T = \frac{4 m g}{3}$

$m g - T = \frac{m g}{4}$

For S $a = \frac{g}{3}, T - m g = \frac{m g}{3}$

$T = \frac{4 m g}{3}$

$2 T = \frac{8 m g}{3}$

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