A block of mass m is kept on a platform Platform starts moving upwards with an acceleration of `g/2` . Find the work done by the normal force on the block in the first one second.

Options

A. `(3mg^2)/2`
B. zero
C. `(3mg^2)/8`
D. `(3mg^2)/4`

Answer

To solve the problem of finding the work done by the normal force on a block of mass \( m \) resting on a platform that accelerates upwards with an acceleration of \( \frac{g}{2} \), we can follow these steps:

### Step 1: Determine the distance traveled by the block in the first second.
Using the second equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]
Here, the initial velocity \( u = 0 \), acceleration \( a = \frac{g}{2} \), and time \( t = 1 \) second.

Substituting the values:
\[ s = 0 \cdot 1 + \frac{1}{2} \cdot \frac{g}{2} \cdot (1)^2 = \frac{1}{2} \cdot \frac{g}{2} = \frac{g}{4} \]

### Step 2: Calculate the normal force acting on the block.
The forces acting on the block are:
- The normal force \( N \) acting upwards.
- The weight of the block \( mg \) acting downwards.

According to Newton's second law, the net force acting on the block is equal to the mass times its acceleration:
\[ N - mg = ma \]
Substituting \( a = \frac{g}{2} \):
\[ N - mg = m \cdot \frac{g}{2} \]
Rearranging gives:
\[ N = mg + m \cdot \frac{g}{2} = mg + \frac{mg}{2} = \frac{3mg}{2} \]

### Step 3: Calculate the work done by the normal force.
The work done \( W \) by the normal force is given by:
\[ W = F \cdot s \]
Where \( F \) is the normal force and \( s \) is the distance traveled.

Substituting the values:
\[ W = N \cdot s = \left(\frac{3mg}{2}\right) \cdot \left(\frac{g}{4}\right) = \frac{3mg^2}{8} \]

### Final Answer:
The work done by the normal force on the block in the first one second is:
\[ W = \frac{3mg^2}{8} \]

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