Energy In Simple Harmonic Motion

The correct answer is 50.

Step 1: Calculate initial and final binding energies - Initial binding energy Final binding energy

Step 2: Calculate the gain in binding energy - Gain in binding energy is given by:

Final Answer: The total gain in binding energy is 121 MeV.

In Simple Harmonic Motion, the displacement of the particle can be represented as: Where is the amplitude of the motion. The potential energy and kinetic energy in SHM are given by the equations: Substitute into the equations: Now, find the ratio of to : Thus, the ratio of potential energy to kinetic energy is .

Solution:
For the 5th harmonic in a closed organ pipe, the relationship between the frequency , speed of sound , and the length of the pipe is given by: Given:
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Substitute the given values into the equation: Solving for : Thus, the length of the organ pipe is .

The Correct Answer is : 20
Momentum conservation :

Energy conservation :
v

The problem asks to find the value of given the time period of a simple pendulum of a specific length located at a height equal to the Earth's radius ( ) above the Earth's surface.

Concept Used:

The solution involves two key concepts from physics:

1. Time Period of a Simple Pendulum: The time period of a simple pendulum is given by the formula:

where is the length of the pendulum and is the effective acceleration due to gravity at the pendulum's location.

2. Variation of Gravity with Altitude: The acceleration due to gravity at a height above the Earth's surface is related to the acceleration due to gravity on the surface ( ) by:

where is the radius of the Earth.

Step-by-Step Solution:

Step 1: Identify the given values.

Length of the pendulum, .

Height above the Earth's surface, .

Time period of the pendulum, .

Step 2: Calculate the acceleration due to gravity ( ) at the height .

Using the formula for variation of gravity with altitude:

Substitute :

Here, is the acceleration due to gravity at the Earth's surface, which is approximately .

Step 3: Determine the time period of the pendulum at this height using its formula.

The time period is given by:

Substitute the values and :

Step 4: Equate the calculated time period with the given expression for the time period.

We are given . Equating this with our derived expression:

Step 5: Solve the equation for .

Cancel from both sides and square the equation:

Now, solve for :

Final Computation & Result:

Substitute the standard value of to find the numerical value of .

Thus, the value of x is 5 (Nearest Integer)