Forces

Let the masses are m and distance between them is l, then
F=

When mass is transferred to the other then masses will be and .

So new force will be

F′=

=

=

The correct option is (C):

By Hooke's law, we have the relation for the elongation of a wire due to force:

where is the cross-sectional area and is the length of the wire. The elongation is directly proportional to and , and inversely proportional to the area. The change in length is given by:

For the second wire, we can write:

Given that , , and , we have:

Thus, the elongation of the second wire is equal to that of the first wire.

Therefore, the ratio is 1.

The problem at hand involves analyzing the distribution of weight when a heavy iron bar is balanced such that one end is on the ground and the other is resting on a person's shoulder. Here is how we can solve this:

Understanding the Situation:

• The iron bar is static, balanced between the ground and the person's shoulder, making an angle with the horizontal.
• This is a standard physics problem involving equilibrium and the distribution of forces.

Principle Involved:

• When a uniform rod is balanced at two points, the weight of the rod is distributed equally at those two points when the rod is symmetrically placed.
• Therefore, the total weight is shared equally between the contact points, which are the ground and the shoulder of the person.

Solution Steps:

1. Consider the iron bar as a uniform rod. The gravitational force acts at its center of mass, which is at the midpoint of the rod.
2. Since the rod is symmetric and in equilibrium, the supported forces by the ground and the person must be equal to balance the gravitational force acting on it.
3. This results in each support (ground and shoulder) experiencing half of the total weight of the bar.
4. Hence, the weight experienced by the person is .

Conclusion:

• The correct answer is: as the weight of the rod is equally distributed between the ground and the person.

Thus, the weight experienced by the person is option: .

Given:

The resultant force is equal to the larger force:

The magnitude of the resultant is given by:

Substituting the values:

Simplifying:

Rearranging terms:

Therefore:

Given that ,

we have:

The correct answer is :

Step 1: Force Equation for Initial Condition

Let the force be the force acting on the balloon. The force equation for the initial condition (with mass ) is:

Step 2: Force When Mass is Released

The force when the mass is released becomes:

Step 3: Force After Releasing Mass

After releasing mass , the equation becomes:

Step 4: Substitute the Value of

Substituting the value of from the previous equation:

Step 5: Solve for

Solving for :

Final Answer: