Ablock of mass m = 15 kg is suspended in an elevator with the help of three identical light elastic cords (spring constant k = 100 N/m each) attached vertically. Cord 1 is tied to the ceiling of the elevator and the other two cords 2 and 3 are tied to the elevator floor as shown in the figure. When the elevator is stationary the tension force in each of the lower cords is T = 7.5 N. Take g = 10 $m / s^{2}$ . If now the elevator starts moving with given four accelerations shown in column I and Column II gives the displacement of the block with respect to elevator when it is accelerating. Column III gives tension in the cords when elevator is accelerating.

Column III represents the tension in chord 2.

(I) (iv) (P)

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(II) (i) (Q)

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(III) (iii) (R)

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(IV) (ii) (S)

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Solution

The correct option is B
(II) (i) (Q)

For elevator acceleration 1 $m / s^{2}$ , tension in cord 2 and cord 3 decreases

So, 165 + $Δ T - 2 \times (7.5 - Δ T) - 150 = (15) (1)$

$\Rightarrow Δ T = 5 N$

$\Rightarrow$ Tension in cord 2, $T_{2} = 2.5 N$

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The correct option is B (II) (i) (Q) For elevator acceleration 1 m/s2, tension in cord 2 and cord 3 decreases So, 165 + ΔT−2×(7.5−ΔT)−150=(15)(1) ⇒ΔT=5N ⇒ Tension in cord 2, T2=2.5 N

The correct option is B
(II) (i) (Q)

For elevator acceleration 1 $m / s^{2}$ , tension in cord 2 and cord 3 decreases

So, 165 + $Δ T - 2 \times (7.5 - Δ T) - 150 = (15) (1)$

$\Rightarrow Δ T = 5 N$

$\Rightarrow$ Tension in cord 2, $T_{2} = 2.5 N$