A spherical body of mass 2kg starting from rest acquires a kinetic of 10000 j at the end of `5^th` second.The force acted on the body is ____N.

Answer

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

### Step 1: Identify the given data
- Mass of the spherical body, \( m = 2 \, \text{kg} \)
- Kinetic energy at the end of the 5th second, \( KE = 10000 \, \text{J} \)
- Initial velocity, \( u = 0 \, \text{m/s} \) (since it starts from rest)

### Step 2: Use the kinetic energy formula
The kinetic energy (KE) of an object is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]
Where \( v \) is the final velocity. We can rearrange this formula to solve for \( v \):
\[ 10000 = \frac{1}{2} \times 2 \times v^2 \]

### Step 3: Simplify the equation
Substituting the mass into the equation:
\[ 10000 = 1 \times v^2 \]
Thus, we have:
\[ v^2 = 10000 \]

### Step 4: Calculate the final velocity
Taking the square root of both sides:
\[ v = \sqrt{10000} = 100 \, \text{m/s} \]

### Step 5: Use the first equation of motion to find acceleration
According to the first equation of motion:
\[ v = u + at \]
Substituting the known values:
\[ 100 = 0 + a \times 5 \]
This simplifies to:
\[ 100 = 5a \]

### Step 6: Solve for acceleration
Dividing both sides by 5:
\[ a = \frac{100}{5} = 20 \, \text{m/s}^2 \]

### Step 7: Calculate the force using Newton's second law
According to Newton's second law, the force \( F \) is given by:
\[ F = ma \]
Substituting the values of mass and acceleration:
\[ F = 2 \times 20 = 40 \, \text{N} \]

### Final Answer
The force acted on the body is \( 40 \, \text{N} \).

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