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A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In each case, the ball will ______
- a)Reach the bottom at the same time
- b)Will take longer time to roll down one plane
- c)Reach the bottom at an unpredictable time
- d)Reach the bottom at the same time and keeps rolling
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A solid sphere rolls down two different inclined planes of the same he...
Introduction:
When a solid sphere rolls down an inclined plane, its motion can be analyzed using the principles of rotational motion and linear motion. The time taken by the sphere to reach the bottom of the inclined plane depends on the angle of inclination and the presence of external forces such as friction. Let's analyze the given options and determine the correct answer.
Analysis:
a) Reach the bottom at the same time:
If the two inclined planes have the same height but different angles of inclination, the time taken by the sphere to reach the bottom will not be the same. This option is incorrect.
b) Will take longer time to roll down one plane:
This option is correct. When the angle of inclination of the plane is larger, the gravitational force component along the inclined plane will be larger. As a result, the sphere will experience a larger torque acting against its rolling motion, causing it to take a longer time to reach the bottom compared to a plane with a smaller angle of inclination.
c) Reach the bottom at an unpredictable time:
The time taken by the sphere to reach the bottom can be predicted based on the principles of physics. Therefore, this option is incorrect.
d) Reach the bottom at the same time and keeps rolling:
The time taken by the sphere to reach the bottom will not be the same for inclined planes with different angles of inclination. Additionally, the sphere will not keep rolling after reaching the bottom due to the presence of friction and other external forces. Therefore, this option is incorrect.
Conclusion:
Based on the analysis, the correct answer is option 'b' - the sphere will take a longer time to roll down one plane compared to the other plane. This is because the larger angle of inclination results in a larger torque opposing the rolling motion, causing the sphere to take more time to reach the bottom.
When a solid sphere rolls down an inclined plane, its motion can be analyzed using the principles of rotational motion and linear motion. The time taken by the sphere to reach the bottom of the inclined plane depends on the angle of inclination and the presence of external forces such as friction. Let's analyze the given options and determine the correct answer.
Analysis:
a) Reach the bottom at the same time:
If the two inclined planes have the same height but different angles of inclination, the time taken by the sphere to reach the bottom will not be the same. This option is incorrect.
b) Will take longer time to roll down one plane:
This option is correct. When the angle of inclination of the plane is larger, the gravitational force component along the inclined plane will be larger. As a result, the sphere will experience a larger torque acting against its rolling motion, causing it to take a longer time to reach the bottom compared to a plane with a smaller angle of inclination.
c) Reach the bottom at an unpredictable time:
The time taken by the sphere to reach the bottom can be predicted based on the principles of physics. Therefore, this option is incorrect.
d) Reach the bottom at the same time and keeps rolling:
The time taken by the sphere to reach the bottom will not be the same for inclined planes with different angles of inclination. Additionally, the sphere will not keep rolling after reaching the bottom due to the presence of friction and other external forces. Therefore, this option is incorrect.
Conclusion:
Based on the analysis, the correct answer is option 'b' - the sphere will take a longer time to roll down one plane compared to the other plane. This is because the larger angle of inclination results in a larger torque opposing the rolling motion, causing the sphere to take more time to reach the bottom.
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Community Answer
A solid sphere rolls down two different inclined planes of the same he...
Acceleration of the rolling sphere,
a = gsinθ/((1+k2/R2))
Velocity of the sphere at the bottom of the inclined plane,
v = √(2gh/((1+k2/R2)))
The sphere will take a longer time to roll down one plane than the other. It will take a larger time in case if the plane with smaller inclination because the acceleration is proportional to sinθ.
a = gsinθ/((1+k2/R2))
Velocity of the sphere at the bottom of the inclined plane,
v = √(2gh/((1+k2/R2)))
The sphere will take a longer time to roll down one plane than the other. It will take a larger time in case if the plane with smaller inclination because the acceleration is proportional to sinθ.
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A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In each case, the ball will ______a)Reach the bottom at the same timeb)Will take longer time to roll down one planec)Reach the bottom at an unpredictable timed)Reach the bottom at the same time and keeps rollingCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In each case, the ball will ______a)Reach the bottom at the same timeb)Will take longer time to roll down one planec)Reach the bottom at an unpredictable timed)Reach the bottom at the same time and keeps rollingCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In each case, the ball will ______a)Reach the bottom at the same timeb)Will take longer time to roll down one planec)Reach the bottom at an unpredictable timed)Reach the bottom at the same time and keeps rollingCorrect answer is option 'B'. Can you explain this answer?.
A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In each case, the ball will ______a)Reach the bottom at the same timeb)Will take longer time to roll down one planec)Reach the bottom at an unpredictable timed)Reach the bottom at the same time and keeps rollingCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In each case, the ball will ______a)Reach the bottom at the same timeb)Will take longer time to roll down one planec)Reach the bottom at an unpredictable timed)Reach the bottom at the same time and keeps rollingCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In each case, the ball will ______a)Reach the bottom at the same timeb)Will take longer time to roll down one planec)Reach the bottom at an unpredictable timed)Reach the bottom at the same time and keeps rollingCorrect answer is option 'B'. Can you explain this answer?.
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