A body of mass 5 kg is raised vertically to a height of 10 m by a force 170 N. The velocity of the body at this height will be

Options

A. 9.8 `ms^(-1)`
B. 15 `ms^(-1)`
C. 22 `ms^(-1)`
D. 37 `ms^(-1)`

Explanation

To solve the problem of finding the velocity of a body of mass 5 kg raised vertically to a height of 10 m by a force of 170 N, we can follow these steps:

### Step 1: Identify the forces acting on the body
The two main forces acting on the body are:
- The upward force (F) = 170 N
- The downward gravitational force (Weight) = mass × gravitational acceleration = 5 kg × 9.8 m/s² = 49 N

### Step 2: Calculate the net force acting on the body
The net force (F_net) acting on the body can be calculated as:
\[ F_{net} = F - Weight = 170 \, \text{N} - 49 \, \text{N} = 121 \, \text{N} \]

### Step 3: Calculate the work done by the net force
The work done (W) by the net force when the body is raised to a height (h) of 10 m is given by:
\[ W = F_{net} \times h = 121 \, \text{N} \times 10 \, \text{m} = 1210 \, \text{J} \]

### Step 4: Relate work done to change in kinetic energy
According to the work-energy theorem, the work done on the body is equal to the change in kinetic energy (ΔKE):
\[ W = KE_{final} - KE_{initial} \]
Since the body starts from rest, \( KE_{initial} = 0 \):
\[ 1210 \, \text{J} = KE_{final} \]

### Step 5: Express kinetic energy in terms of velocity
The kinetic energy (KE) can be expressed as:
\[ KE = \frac{1}{2} m v^2 \]
Substituting for \( KE_{final} \):
\[ 1210 = \frac{1}{2} \times 5 \times v^2 \]

### Step 6: Solve for velocity (v)
Rearranging the equation to solve for \( v^2 \):
\[ 1210 = \frac{5}{2} v^2 \]
\[ v^2 = \frac{1210 \times 2}{5} = \frac{2420}{5} = 484 \]
Taking the square root to find \( v \):
\[ v = \sqrt{484} = 22 \, \text{m/s} \]

### Conclusion
The velocity of the body at the height of 10 m is approximately 22 m/s.

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