Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A gardener pulls a lawn roller along the ground through a distance of 20 m. If he applies a force of 20 kg wt in a direction inclined at 60º to the ground, find the work done by him. (Take g = 10 m/s 2 )
Text Solution
Verified by ExpertsThe correct answer is:
B
Step 1: Convert the force from kg wt to Newtons.
The weight force can be calculated using the formula:
\( F = m \cdot g \)
Given that the mass (m) is 20 kg and \( g = 10 \, m/s^2 \), the force in Newtons is:
\( F = 20 \, kg \times 10 \, m/s^2 = 200 \, N \)
Step 2: Calculate the component of the force that does work.
The work done (W) is given by the formula:
\( W = F \cdot d \cdot \cos(\theta) \)
where
- \( F = 200 \, N \) (the force applied),
- \( d = 20 \, m \) (the distance moved), and
- \( \theta = 60º \) (the angle of inclination).
Step 3: Substitute the values into the work equation.
\( W = 200 \, N \times 20 \, m \times \cos(60º) \)
Note: \( \cos(60º) = \frac{1}{2} \)
\( W = 200 \times 20 \times \frac{1}{2} \)
\( W = 200 \times 10 \)
\( W = 2000 \, J \)
Therefore, the work done by the gardener is 2000 Joules.
The weight force can be calculated using the formula:
\( F = m \cdot g \)
Given that the mass (m) is 20 kg and \( g = 10 \, m/s^2 \), the force in Newtons is:
\( F = 20 \, kg \times 10 \, m/s^2 = 200 \, N \)
Step 2: Calculate the component of the force that does work.
The work done (W) is given by the formula:
\( W = F \cdot d \cdot \cos(\theta) \)
where
- \( F = 200 \, N \) (the force applied),
- \( d = 20 \, m \) (the distance moved), and
- \( \theta = 60º \) (the angle of inclination).
Step 3: Substitute the values into the work equation.
\( W = 200 \, N \times 20 \, m \times \cos(60º) \)
Note: \( \cos(60º) = \frac{1}{2} \)
\( W = 200 \times 20 \times \frac{1}{2} \)
\( W = 200 \times 10 \)
\( W = 2000 \, J \)
Therefore, the work done by the gardener is 2000 Joules.
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