A body of mass 60 kg is dragged with just enough force to start moving on a rough surface with coefficient of static and kinetic frictions `0.5` and `0.4` respectively . On applying the same force , what is the acceleration ?

Options

A. `0.98m//s^(2)`
B. `9.8 m//s^(2)`
C. `0.54m//s^(2)`
D. `5.292m//s^(2)`

Answer

To solve the problem step by step, we will follow the physics principles related to friction and Newton's laws of motion.

### Step 1: Identify the forces acting on the body
The body has a mass \( m = 60 \, \text{kg} \). The forces acting on the body include:
- The gravitational force \( F_g = mg \)
- The normal force \( N \)
- The static friction force \( F_{s} \) when the body is at rest
- The kinetic friction force \( F_{k} \) when the body is in motion

### Step 2: Calculate the gravitational force
The gravitational force can be calculated as:
\[ F_g = mg = 60 \, \text{kg} \times 10 \, \text{m/s}^2 = 600 \, \text{N} \]

### Step 3: Determine the normal force
Since the body is on a horizontal surface and there are no vertical forces acting other than gravity and the normal force, we have:
\[ N = F_g = 600 \, \text{N} \]

### Step 4: Calculate the maximum static friction force
The maximum static friction force \( F_{s \text{max}} \) can be calculated using the coefficient of static friction \( \mu_s = 0.5 \):
\[ F_{s \text{max}} = \mu_s \times N = 0.5 \times 600 \, \text{N} = 300 \, \text{N} \]

### Step 5: Determine the force applied to start the motion
The force applied to just start moving the body is equal to the maximum static friction force:
\[ F = F_{s \text{max}} = 300 \, \text{N} \]

### Step 6: Calculate the kinetic friction force once the body is in motion
Once the body starts moving, we need to consider the kinetic friction force \( F_k \) using the coefficient of kinetic friction \( \mu_k = 0.4 \):
\[ F_k = \mu_k \times N = 0.4 \times 600 \, \text{N} = 240 \, \text{N} \]

### Step 7: Calculate the net force acting on the body
The net force \( F_{net} \) acting on the body after it starts moving is the applied force minus the kinetic friction force:
\[ F_{net} = F - F_k = 300 \, \text{N} - 240 \, \text{N} = 60 \, \text{N} \]

### Step 8: Calculate the acceleration of the body
Using Newton's second law \( F = ma \), we can find the acceleration \( a \):
\[ a = \frac{F_{net}}{m} = \frac{60 \, \text{N}}{60 \, \text{kg}} = 1 \, \text{m/s}^2 \]

### Final Answer
The acceleration of the body after it starts moving is:
\[ \boxed{1 \, \text{m/s}^2} \]