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A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom starting from rest at the top. How much time does it take to cover one-fourth distance starting from rest at the top
- a)1 s
- b)4 s
- c)2s
- d)16 s
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A body sliding on a smooth inclined plane requires 4 seconds to reach ...
Given information:
- A body is sliding on a smooth inclined plane.
- The body takes 4 seconds to reach the bottom starting from rest at the top.
To find:
How much time does it take to cover one-fourth distance starting from rest at the top?
Solution:
To solve this problem, we can use the concept of time and distance.
Step 1: Understanding the motion of the body
- The body starts from rest at the top of the inclined plane.
- It accelerates due to the force of gravity while sliding down the plane.
- At the bottom of the plane, the body reaches its maximum speed and stops accelerating.
- The body covers a certain distance in a given time period.
Step 2: Analyzing the given information
- The body takes 4 seconds to cover the entire distance from the top to the bottom.
- Therefore, the total time taken is 4 seconds.
- We need to find the time taken to cover one-fourth of the distance.
Step 3: Calculating the time taken to cover one-fourth distance
- Let's assume the total distance from the top to the bottom is D.
- The time taken to cover one-fourth of the distance is T.
- We know that the time taken to cover a certain distance is directly proportional to the square root of that distance.
- Therefore, we can write the equation as:
(T/4)^0.5 = 4^0.5 (since T/4 is one-fourth of the total distance, and 4 is the total time taken)
- Simplifying the equation, we get:
T/4 = 4
T = 4 * 4
T = 16 seconds
Step 4: Conclusion
- The time taken to cover one-fourth distance starting from rest at the top is 16 seconds.
- A body is sliding on a smooth inclined plane.
- The body takes 4 seconds to reach the bottom starting from rest at the top.
To find:
How much time does it take to cover one-fourth distance starting from rest at the top?
Solution:
To solve this problem, we can use the concept of time and distance.
Step 1: Understanding the motion of the body
- The body starts from rest at the top of the inclined plane.
- It accelerates due to the force of gravity while sliding down the plane.
- At the bottom of the plane, the body reaches its maximum speed and stops accelerating.
- The body covers a certain distance in a given time period.
Step 2: Analyzing the given information
- The body takes 4 seconds to cover the entire distance from the top to the bottom.
- Therefore, the total time taken is 4 seconds.
- We need to find the time taken to cover one-fourth of the distance.
Step 3: Calculating the time taken to cover one-fourth distance
- Let's assume the total distance from the top to the bottom is D.
- The time taken to cover one-fourth of the distance is T.
- We know that the time taken to cover a certain distance is directly proportional to the square root of that distance.
- Therefore, we can write the equation as:
(T/4)^0.5 = 4^0.5 (since T/4 is one-fourth of the total distance, and 4 is the total time taken)
- Simplifying the equation, we get:
T/4 = 4
T = 4 * 4
T = 16 seconds
Step 4: Conclusion
- The time taken to cover one-fourth distance starting from rest at the top is 16 seconds.
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