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CGP EDU Academic Team
Published on: September 12, 2026
A body of mass 100 g is rotating in a circular path of radius r with constant speed. The work done in one complete revolution is.
Text Solution
Verified by ExpertsThe correct answer is:
D
Step 1: Understand what work done means in a circular motion. In circular motion, the direction of the velocity of the body is continuously changing, while its speed remains constant.
Step 2: Work done is defined mathematically as the dot product of force and displacement:
$$W = F imes d imes ext{cos}( heta)$$ where $F$ is the force exerted, $d$ is the displacement, and $ heta$ is the angle between the force and displacement vectors.
Step 3: In uniform circular motion, the centripetal force acts towards the center of the circular path. The displacement in one complete revolution is along the circular path, which is perpendicular to the centripetal force.
Step 4: Because the angle between the centripetal force and the displacement vector is 90 degrees, the cosine term becomes zero:
$$ ext{cos}(90^ ext{o}) = 0$$.
Step 5: Thus, the work done in one complete revolution is:
$$W = F imes d imes 0 = 0$$.
Conclusion: Therefore, the work done in one complete revolution is zero.
Step 2: Work done is defined mathematically as the dot product of force and displacement:
$$W = F imes d imes ext{cos}( heta)$$ where $F$ is the force exerted, $d$ is the displacement, and $ heta$ is the angle between the force and displacement vectors.
Step 3: In uniform circular motion, the centripetal force acts towards the center of the circular path. The displacement in one complete revolution is along the circular path, which is perpendicular to the centripetal force.
Step 4: Because the angle between the centripetal force and the displacement vector is 90 degrees, the cosine term becomes zero:
$$ ext{cos}(90^ ext{o}) = 0$$.
Step 5: Thus, the work done in one complete revolution is:
$$W = F imes d imes 0 = 0$$.
Conclusion: Therefore, the work done in one complete revolution is zero.
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