Question

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the extension of an elastic spring is found to vary directly with the weight suspended from it. if a way out of 75 kg produces an extension of 1.4 cm , calculate the weight that would produce an extension of of 9.8 CM .
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Answer 1

Step-by-step explanation:

Solution:-

Given,

the extension of an elastic spring found to vary directly with the weight suspended from it

so write

l \alpha wlαw

=> l = kw (1)

where k = proprotionally constant

l = represent the extension of an elastic spring

w =represent the weight

w = 75kg

l= 1.4 cm

so substitute these vale In equation (1)

we have 1.4 = k× 75

k =1.4/ 75

so equation (1) becomes

l =1.4/75 × w

when l = 9.8 cm = 1.4 / 75 × w

=> w = 9.8 × 75 / 1.4 = 525 kg

hence w = 525 kg , l = 9.8 cm

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Answer 2

Step-by-step explanation:

$\bf\ 1 \: kg = 1000gm \\ \\ \bf\ \: 75kg = 75000g \\ \\ </p><p> \bf\ Extension = 14/10 \\ \\ \bf\ </p><p>In \: second \: case \: </p><p> Weight = x \\ \\ \bf\ </p><p>Extension = 98/10 \\ \\ \sf\ \implies: 75000 \times \frac{98}{10} = \frac{14}{10} \bf\ x </p><p> \\ \\ \\ \bf\red{ Multiplying \: both \: sides \: with \: 10 \: } \\ \\ \sf\ \implies:7350000 = 14x</p><p> \\ \\\sf\ \implies: 7350000 = 14x \\ \\ \sf\ \implies: 14x = 7350000 \\ \\ </p><p>\sf\ \implies: x = 7350000/14 \\ \\ </p><p>\sf\ \implies: x = 525000 \\ \\ \bf\pink{ In \: gram, \: x = 525000 gm} \\ \\ \bf\purple{ </p><p>In \: kilograms, x = 525 kg}</p><p></p><p>$