At a place where the acceleration due to gravity is `10"m sec"^(-2)` a force of 5 kg - wt acts on a body of mass 10 kg initially at rest. The velocity of the body after 4 second is

Options

A. 5 m/s
B. 20 m/s
C. 10 m/s
D. 50 m/s

Answer

To solve the problem step by step, we will follow the principles of Newton's laws of motion.

### Step 1: Understand the Given Information
- The acceleration due to gravity \( g = 10 \, \text{m/s}^2 \)
- Force acting on the body \( F = 5 \, \text{kg-wt} \)
- Mass of the body \( m = 10 \, \text{kg} \)
- Initial velocity \( u = 0 \, \text{m/s} \) (the body is initially at rest)
- Time \( t = 4 \, \text{s} \)

### Step 2: Convert the Force from kg-wt to Newtons
The force in kg-wt can be converted to Newtons using the relation:
\[ 1 \, \text{kg-wt} = g \, \text{N} \]
Thus,
\[ F = 5 \, \text{kg-wt} = 5 \times 10 \, \text{N} = 50 \, \text{N} \]

### Step 3: Calculate the Acceleration
Using Newton's second law, the acceleration \( a \) can be calculated using the formula:
\[ a = \frac{F}{m} \]
Substituting the values:
\[ a = \frac{50 \, \text{N}}{10 \, \text{kg}} = 5 \, \text{m/s}^2 \]

### Step 4: Use the Equation of Motion to Find Final Velocity
We can use the first equation of motion to find the final velocity \( v \):
\[ v = u + at \]
Substituting the known values:
\[ v = 0 + (5 \, \text{m/s}^2)(4 \, \text{s}) = 20 \, \text{m/s} \]

### Final Answer
The velocity of the body after 4 seconds is \( 20 \, \text{m/s} \).

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