A constant horizontal force of 20N acts on a body on a smooth horizontal plane. The body starts from rest and is observed to move 20 m in two seconds. The mass of the body is

Options

A. 4 kg
B. 2 kg
C. 1 kg
D. 0.5 kg

Answer

To solve the problem step by step, we will follow the principles of kinematics and Newton's second law of motion.

### Step 1: Identify the given information
- A constant horizontal force \( F = 20 \, \text{N} \)
- Distance \( d = 20 \, \text{m} \)
- Time \( t = 2 \, \text{s} \)
- Initial velocity \( u = 0 \, \text{m/s} \) (the body starts from rest)

### Step 2: Calculate the acceleration
Using the formula for distance in uniformly accelerated motion:
\[ d = ut + \frac{1}{2} a t^2 \]
Since the initial velocity \( u = 0 \):
\[ d = \frac{1}{2} a t^2 \]
Substituting the known values:
\[ 20 = \frac{1}{2} a (2^2) \]
This simplifies to:
\[ 20 = \frac{1}{2} a \cdot 4 \]
\[ 20 = 2a \]
Now, solving for \( a \):
\[ a = \frac{20}{2} = 10 \, \text{m/s}^2 \]

### Step 3: Apply Newton's second law of motion
Newton's second law states:
\[ F = m \cdot a \]
Where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration. We can rearrange this to find the mass:
\[ m = \frac{F}{a} \]
Substituting the values we have:
\[ m = \frac{20 \, \text{N}}{10 \, \text{m/s}^2} \]
Calculating this gives:
\[ m = 2 \, \text{kg} \]

### Conclusion
The mass of the body is \( 2 \, \text{kg} \).

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