A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this spring, when displaced and released, oscillates with a period of 0.6s. What is the weight of the body? When 50 kg is put, the extension of spring is 20 cm.

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the relationship between force, spring constant, and extension
The force exerted by a spring is given by Hooke's Law:
\[ F = k \cdot x \]
where:
- \( F \) is the force applied (in Newtons),
- \( k \) is the spring constant (in Newtons per meter),
- \( x \) is the extension of the spring (in meters).

### Step 2: Calculate the spring constant \( k \)
We know that when a mass of 50 kg is attached to the spring, it causes an extension of 20 cm (0.2 m). The weight \( W \) of the mass is given by:
\[ W = m \cdot g \]
where \( g \approx 9.8 \, \text{m/s}^2 \). Thus,
\[ W = 50 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 490 \, \text{N} \]

Now we can substitute \( F \) and \( x \) into Hooke's Law:
\[ 490 \, \text{N} = k \cdot 0.2 \, \text{m} \]
Solving for \( k \):
\[ k = \frac{490 \, \text{N}}{0.2 \, \text{m}} = 2450 \, \text{N/m} \]

### Step 3: Use the period of oscillation to find the mass of the body
The period \( T \) of a mass-spring system is given by:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
Squaring both sides gives:
\[ T^2 = 4\pi^2 \frac{m}{k} \]
Rearranging to find \( m \):
\[ m = \frac{T^2 \cdot k}{4\pi^2} \]

Substituting the known values:
- \( T = 0.6 \, \text{s} \)
- \( k = 2450 \, \text{N/m} \)

Calculating \( m \):
\[ m = \frac{(0.6)^2 \cdot 2450}{4 \cdot (3.14)^2} \]
Calculating \( (0.6)^2 = 0.36 \):
\[ m = \frac{0.36 \cdot 2450}{4 \cdot 9.8596} \]
Calculating \( 4 \cdot 9.8596 \approx 39.4384 \):
\[ m = \frac{882}{39.4384} \approx 22.36 \, \text{kg} \]

### Step 4: Calculate the weight of the body
The weight \( W \) of the body is given by:
\[ W = m \cdot g \]
Substituting the values:
\[ W = 22.36 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \]
Calculating:
\[ W \approx 219.1 \, \text{N} \]

### Final Answer
The weight of the body is approximately **219.1 N**.

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