Question

The work done in moving a body of mass 2 kg to a height of 4 m from the surface of the earth is: (Acceleration due to gravity = 10 ms\(^{-2}\))

• A. 10 J
• B. 20 J
• C. 40 J
• D. 80 J

Hint:

Work done is the energy transferred when a force is applied to move an object over a distance. In this case, the work is the force of gravity acting on the body as it is lifted to a height.

Answer 1

The Correct Option is D

Step 1: Understanding the concept of work done.
Work done in lifting an object vertically against gravity is calculated using the formula: \[ W = F \times d \] Where:
\( W \) is the work done,
\( F \) is the force applied to the object (in this case, the gravitational force),
\( d \) is the distance moved by the object (in this case, the height it is lifted).
For lifting an object vertically, the force \( F \) is equal to the weight of the object, which is given by: \[ F = mg \] Where:
\( m \) is the mass of the object,
\( g \) is the acceleration due to gravity.
So, the work done can be written as: \[ W = mgh \] Where:
\( m = 2 \, \text{kg} \) (mass of the body),
\( g = 10 \, \text{ms}^{-2} \) (acceleration due to gravity),
\( h = 4 \, \text{m} \) (height).

Step 2: Substitute the given values into the formula.
Now that we know the formula to calculate the work done, we can substitute the values: \[ W = (2 \, \text{kg})(10 \, \text{ms}^{-2})(4 \, \text{m}) \]
Step 3: Perform the calculation.
Multiplying the values: \[ W = 2 \times 10 \times 4 = 80 \, \text{J} \] Thus, the work done in moving the body to a height of 4 m is \( 80 \, \text{J} \). % Final Answer The correct answer is (4) 80 J.