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The natural length of the spring is 60 cm and its spring constant is 4000 N/m. A 20 kg weight is suspended from it. The extension produced by the spring is, (Take g=9.8 m/s2 )

Option: 1

4.9 cm

 


Option: 2

0.49 cm


Option: 3

9.4 cm

 


Option: 4

0.94 cm


Answers (1)

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The extension created in a spring can be calculated using Hooke's law, which states that the force exerted by a spring is directly proportional to the extension created in the spring. Mathematically, this can be represented as:

F=k x

where F is the force exerted by the spring, k is the spring constant, and x is the extension produced by the spring.

To calculate the extension created by the spring in this scenario, we can start by calculating the force exerted by the mass. The force exerted by a mass is equal to its mass, which can be calculated as:

F=m g

where m is the mass and g is the gravitational acceleration (9.8 m/s2).

By substituting the values given in the question, we get:

F=20 kg\times 9.8 \mathrm{~m} / \mathrm{s}^2=196 \mathrm{~N}

We can now use Hooke's law to calculate the extension produced by the spring:

F=k x

\\ x=\frac{F}{k}

By substituting the values given in the question, we get:

x=\frac{196 \mathrm{~N}}{4000 \mathrm{~N} / \mathrm{m}}=0.049 \mathrm{~m}

Therefore, the extension produced in the spring is 0.049 m, or 4.9 cm.

Posted by

Shailly goel

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