A force of 20N is applied on a body of mass 5 kg resting on a horizontal plane. The body gains a kinetic energy of 10 after is moves a distance 2m. The fricitional force is

Options

A. 10N
B. 15N
C. 20N
D. 30N

Explanation

To solve the problem, we need to find the frictional force acting on a body when a force is applied to it. Here’s a step-by-step solution:

### Step 1: Identify the given data
- Applied force (F) = 20 N
- Mass of the body (m) = 5 kg
- Kinetic energy gained (KE) = 10 J
- Distance moved (s) = 2 m

### Step 2: Use the kinetic energy formula to find the velocity
The formula for kinetic energy is given by:

\[ KE = \frac{1}{2} m v^2 \]

Substituting the known values:

\[ 10 = \frac{1}{2} \times 5 \times v^2 \]

This simplifies to:

\[ 10 = \frac{5}{2} v^2 \]

Multiplying both sides by 2:

\[ 20 = 5 v^2 \]

Now, dividing both sides by 5:

\[ v^2 = 4 \]

Taking the square root:

\[ v = 2 \text{ m/s} \]

### Step 3: Calculate the acceleration using the kinematic equation
We can use the equation of motion:

\[ v^2 = u^2 + 2as \]

Where:
- \(v\) = final velocity = 2 m/s
- \(u\) = initial velocity = 0 m/s (since the body is at rest)
- \(s\) = distance = 2 m

Substituting the values:

\[ 4 = 0 + 2a \times 2 \]

This simplifies to:

\[ 4 = 4a \]

Dividing both sides by 4:

\[ a = 1 \text{ m/s}^2 \]

### Step 4: Apply Newton's second law to find the frictional force
According to Newton's second law, the net force acting on the body is given by:

\[ F_{\text{net}} = m \cdot a \]

Where:
- \(F_{\text{net}} = F - F_f\) (where \(F_f\) is the frictional force)

Substituting the known values:

\[ F_{\text{net}} = 5 \cdot 1 = 5 \text{ N} \]

Now, we know that:

\[ F_{\text{net}} = F - F_f \]

Substituting the values:

\[ 5 = 20 - F_f \]

Rearranging gives:

\[ F_f = 20 - 5 = 15 \text{ N} \]

### Final Answer
The frictional force acting on the body is **15 N**.

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