A mass of 1 kg is suspended by means of a thread. The system is (i) lifted up with an acceleration of 4.9 $m s^{2}$ (ii) lowered with an acceleration of 4.9 $m s^{- 2}$ . The ratio of tension in the first and second case is:

3: 1

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1: 2

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1: 3

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2: 1

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Solution

The correct option is A 3: 1
Case I:
Using Newton's second law of motion,
$T_{1} - m g = m a$
$T_{1} = m (g + a)$ ........(i)
Case II:
Using Newton's second law of motion,
$m g - T_{2} = m a$
$T_{2} = m (g - a)$ ..............(ii)
From equation (i) and (ii)

$\frac{T_{1}}{T_{2}} = \frac{g + a}{g - a} = \frac{9.8 + 4.9}{9.8 - 4.9} = \frac{3}{1}$

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