A mass of 10 gm is suspended by a string and the entire system is falling with a uniform acceleration of . `400cm//sec^(2)` The tension in the string will be `(g=980cm//sec^(2))`

Options

A. 5,800 dyne
B. 9,800 dyne
C. 11,800 dyne
D. 13,800 dyne

Answer

To find the tension in the string when a mass of 10 grams is suspended and the entire system is falling with a uniform acceleration of 400 cm/s², we can use the following steps:

### Step 1: Identify the known values
- Mass (m) = 10 grams = 0.01 kg (though we will use grams in our calculations since the other values are in CGS units)
- Acceleration due to gravity (g) = 980 cm/s²
- Acceleration of the falling system (a) = 400 cm/s²

### Step 2: Write the equation for tension
The tension (T) in the string can be calculated using the formula:
\[ T = mg - ma \]
Where:
- \( mg \) is the weight of the mass,
- \( ma \) is the effective force due to the acceleration of the system.

### Step 3: Calculate the weight of the mass (mg)
Using the values:
\[ mg = 10 \, \text{grams} \times 980 \, \text{cm/s}^2 \]
\[ mg = 9800 \, \text{dynes} \]

### Step 4: Calculate the force due to acceleration (ma)
Using the values:
\[ ma = 10 \, \text{grams} \times 400 \, \text{cm/s}^2 \]
\[ ma = 4000 \, \text{dynes} \]

### Step 5: Substitute the values into the tension formula
Now, substitute \( mg \) and \( ma \) into the tension formula:
\[ T = 9800 \, \text{dynes} - 4000 \, \text{dynes} \]
\[ T = 5800 \, \text{dynes} \]

### Step 6: Conclusion
The tension in the string is:
\[ T = 5800 \, \text{dynes} \]