A vertical scale on a spring balance reads from 0 to 200 N . The scale has a length of 11.0 cm from the 0 to 200 N reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.55 Hz .Ignoring the mass of the spring, what is the mass m of the fish?

7.08 kg

Explanation:

Given:

Length of scale (x) = 11.0 cm = 0.110 m [1 cm = 0.01 m]

Range of scale is from 0 to 200 N.

Frequency of oscillation of fish (f) = 2.55 Hz

Mass of the fish (m) = ?

Now, range of scale is from 0 to 200 N. So, maximum force, the spring can hold is 200 N. For this maximum force, the extension in the spring is equal to the length of the scale. So,

Now, we know that, spring force is given as:

Where, 'k' is spring constant.

Now, plug in the given values and solve for 'k'. This gives,

Now, the oscillation of the fish represents simple harmonic motion as it is attached to the spring.

So, the frequency of oscillation is given as:

Squaring both sides and expressing it in terms of 'm', we get:

Now, plug in the given values and solve for 'm'. This gives,

Therefore, the mass of the fish is 7.08 kg.

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explanation:

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