A body of mass 8 kg is hanging from another body of mass 12 kg. The combination is being pulled up by a string with an acceleration of 2.2 m/sec2. The tension T1 will be -

Options

A. 260N
B. 240N
C. 220N
D. 200N

Answer

To find the tension \( T_1 \) in the string that is pulling the combination of two bodies (one of mass 8 kg and the other of mass 12 kg) upwards with an acceleration of \( 2.2 \, \text{m/s}^2 \), we can follow these steps:

### Step 1: Determine the total mass of the system
The total mass \( M \) of the system is the sum of the masses of both bodies:
\[ M = m_1 + m_2 = 8 \, \text{kg} + 12 \, \text{kg} = 20 \, \text{kg} \]

### Step 2: Calculate the weight of the system
The weight \( W \) of the system can be calculated using the formula:
\[ W = M \cdot g \]
where \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)):
\[ W = 20 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 196 \, \text{N} \]

### Step 3: Apply Newton's second law
According to Newton's second law, the net force \( F_{\text{net}} \) acting on the system is equal to the mass times the acceleration:
\[ F_{\text{net}} = M \cdot a \]
Substituting the values we have:
\[ F_{\text{net}} = 20 \, \text{kg} \cdot 2.2 \, \text{m/s}^2 = 44 \, \text{N} \]

### Step 4: Determine the tension in the string
The tension \( T_1 \) in the string must overcome both the weight of the system and provide the necessary net force for the upward acceleration. Therefore, we can write:
\[ T_1 - W = F_{\text{net}} \]
Rearranging gives us:
\[ T_1 = W + F_{\text{net}} \]
Substituting the values we calculated:
\[ T_1 = 196 \, \text{N} + 44 \, \text{N} = 240 \, \text{N} \]

### Conclusion
The tension \( T_1 \) in the string is \( 240 \, \text{N} \).

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