Distance And Displacement

To solve this problem, we need to determine the relationship between the time taken to fall the first half of the distance and the second half of the distance for a freely falling ball (under gravity). Let's break down the solution step-by-step:

1. We are given that a ball is released from a height . When the ball is dropped from a height, it accelerates downwards under the influence of gravity, .
2. The time taken to cover the first half of the distance is . Using the kinematic equation for uniformly accelerated motion: , where .
3. Plugging into the equation, we get: . Simplifying, we find: .
4. For the second half, time taken is . The ball has traveled a total distance of within a total time , where .
5. At the midpoint (first ), using , we know: .
6. Using the known fact for falling objects, , approximately: , which becomes .
7. Thus, .

Therefore, the correct relationship is .

The correct answer is 2

For F to be maximum 

So, the correct answer is

Step 1: Identify the Slopes

The slope of A is given as:

The slope of B is given as:

Step 2: Compare the Slopes

Since:

It follows that:

Step 3: Relate Velocity to Time

As velocity ( ) is inversely related to time ( ) for a given distance:

Conclusion:

The final answer is: (A) and (E) only.

Step 1: Electric Field Due to Infinite Sheet
The electric field due to an infinite sheet charge is given by: Step 2: Electric Field Due to Infinite Line Charge
The electric field due to an infinite line charge at a perpendicular distance is given by: Step 3: Electric Fields at Points 'P' and 'Q'
For point 'P', the distance from the line charge is . The resultant electric field is: For point 'Q', the distance from the line charge is . The resultant electric field is: Step 4: Ratio of Electric Fields
The ratio is given by: Substitute , , and : Step 5: Simplify the Expression
Simplify the numerator and denominator: Combine the terms: Simplify further: Equating , solve for :

To determine the distance above and below the Earth's surface where a body has the same weight, we need to understand the concept of gravitational force variation above and below the Earth's surface.

The gravitational force experienced by a body at a distance above or below the Earth's surface can be expressed using the formula for gravitational force:

1. Above the Earth's surface:

The gravitational force at a height above the Earth's surface:

2. Below the Earth's surface:

The gravitational force at a depth below the Earth's surface:

We are given that these forces are equal, so:

By simplifying, we cancel out from both sides and solve for in terms of :

Simplifying further, we obtain:

Let because they need to be symmetric for the weight to be the same. Hence the equation becomes:

Solving this quadratic equation for , we find:

This means that the body will have the same weight at a distance both above and below the Earth's surface. Therefore, the correct answer is .

This comprehensive solution confirms that the option is correct.