The work done in pushing a block of mass 10 kg from bottom to the top of a frictionless inclined plane 5 m long and 3 m high is-
`(g=9.8m//sec^(2))`

Options

A. 392 J
B. 294 J
C. 98 J
D. 0.98 J

Answer

To solve the problem of calculating the work done in pushing a block of mass 10 kg from the bottom to the top of a frictionless inclined plane that is 5 m long and 3 m high, we can follow these steps:

### Step 1: Identify the parameters
- Mass of the block (m) = 10 kg
- Height of the inclined plane (h) = 3 m
- Acceleration due to gravity (g) = 9.8 m/s²

### Step 2: Calculate the work done
Since the inclined plane is frictionless, the work done on the block is equal to the change in potential energy as it is raised to a height \( h \). The formula for gravitational potential energy (PE) is given by:

\[ PE = m \cdot g \cdot h \]

### Step 3: Substitute the values into the formula
Now, substituting the known values into the potential energy formula:

\[ PE = 10 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 3 \, \text{m} \]

### Step 4: Perform the multiplication
Calculating the above expression step by step:

1. First, calculate \( 10 \cdot 9.8 \):

\[ 10 \cdot 9.8 = 98 \, \text{kg m/s}^2 \]

2. Now, multiply this result by the height (3 m):

\[ 98 \cdot 3 = 294 \, \text{Joules} \]

### Step 5: Conclusion
Thus, the work done in pushing the block to the top of the inclined plane is:

\[ \text{Work Done} = 294 \, \text{Joules} \]

### Final Answer
The work done in pushing the block is **294 Joules**.

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