A force of 72 dyne is inclined to the horizontal at an angle of `60^(@)`. Find the acceleration in a mass of 9 g, which moves in a horizontal direction.

Options

A. `5 cms^(-1)`
B. ` 4 cms^(-1)`
C. `2ms^(-1)`
D. `3 ms^(-1)`

Explanation

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

### Step 1: Identify the Given Values
- Force (F) = 72 dyne
- Angle (θ) = 60 degrees
- Mass (m) = 9 g

### Step 2: Resolve the Force into Components
The force can be resolved into two components:
- Horizontal component (F_x) = F * cos(θ)
- Vertical component (F_y) = F * sin(θ)

For our case:
- F_x = 72 dyne * cos(60°)
- F_y = 72 dyne * sin(60°)

### Step 3: Calculate the Horizontal Component of the Force
Using the cosine value:
- cos(60°) = 1/2

Thus,
- F_x = 72 dyne * (1/2) = 36 dyne

### Step 4: Apply Newton's Second Law
According to Newton's second law, the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). Since we are interested in the horizontal motion:
- F_x = m * a

### Step 5: Convert Mass to Appropriate Units
We need to convert the mass from grams to kilograms for standard SI units. However, since we are using dyne (where 1 dyne = 1 g·cm/s²), we can keep it in grams.
- m = 9 g

### Step 6: Rearrange the Equation to Solve for Acceleration (a)
From the equation F_x = m * a, we can rearrange it to find acceleration:
- a = F_x / m

### Step 7: Substitute the Values
Now substitute the values we have:
- a = 36 dyne / 9 g

### Step 8: Calculate the Acceleration
- a = 4 cm/s²

### Final Answer
Thus, the acceleration of the mass is **4 cm/s²**.

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