A spring of force constant 800 N/m has an extension of 5 cm. The work done in extending it from 5 cm to 15 cm is
(a) 16 J
(b) 8 J
(c) 32 J
(d) 24 J
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it's answer should be 4
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Answer:
B) 8J
Explanation:
Constant = 800N/m
Extension = 5cm
The work done will be stored as elastic potential energy in the spring.
Thus,
W = 1/2 × k ( x₂² - x₁²), where
x₁ = 5 cm and x₂ = 15 cm
Force constant, k = 800 N/m = 800/100 N/cm = 8 N/cm
W = 1/2 × 8 (15² - 5²)
= 1/2 × 8 ( 225 - 25)
= 1/2 × 8 × 200 = 800 N cm
W = 800 N cm = 8 N m = 8 J
Therefore, the work done in extending it from 5cm to 15cm is 8 J.
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