A block of mass 5 kg is resting on a smooth surface at what angle a force of 20 N be acted on the body so that it will acquire a kinetic energy of 40 J after moving 4 m?

Options

A. `30^0`
B. `45^0`
C. `60^0`
D. `120^0`

Answer

To solve the problem, we need to determine the angle at which a force of 20 N must be applied to a 5 kg block so that it acquires a kinetic energy of 40 J after moving 4 m.

### Step-by-Step Solution:

1. **Understand the Problem**:
We have a block of mass \( m = 5 \, \text{kg} \) resting on a smooth surface. A force \( F = 20 \, \text{N} \) is applied at an angle \( \theta \) to the direction of displacement. The block moves a distance \( d = 4 \, \text{m} \) and acquires a kinetic energy \( KE = 40 \, \text{J} \).

2. **Apply the Work-Energy Principle**:
According to the work-energy principle, the work done on the block is equal to the change in its kinetic energy:
\[ W = \Delta KE \]
Since the block starts from rest, the initial kinetic energy is 0. Therefore:
\[ W = KE = 40 \, \text{J} \]

3. **Calculate the Work Done**:
The work done by the force can be expressed as:
\[ W = F \cdot d \cdot \cos(\theta) \]
Substituting the known values:
\[ 40 = 20 \cdot 4 \cdot \cos(\theta) \]

4. **Simplify the Equation**:
Simplifying the equation gives:
\[ 40 = 80 \cdot \cos(\theta) \]
Dividing both sides by 80:
\[ \cos(\theta) = \frac{40}{80} = \frac{1}{2} \]

5. **Find the Angle**:
The angle \( \theta \) for which \( \cos(\theta) = \frac{1}{2} \) is:
\[ \theta = 60^\circ \]

6. **Conclusion**:
Therefore, the angle at which the force must be applied is \( 60^\circ \).

### Final Answer:
The angle \( \theta \) is \( 60^\circ \).