Home
Class 11
PHYSICS
The relation between acceleration and di...

The relation between acceleration and displacement of four particles are given below. The particle undergoing SHM is:

A

`a_(x)=+2x`

B

`a_(x)=+2x^(2)`

C

`a_(x)=-2x^(2)`

D

`a_(x)=-2x`

Text Solution

AI Generated Solution

The correct Answer is:
To determine which particle is undergoing simple harmonic motion (SHM) based on the given relations between acceleration (a) and displacement (x), we can analyze the provided equations step by step. ### Step-by-Step Solution: 1. **Understanding the Relation of Acceleration and Displacement**: - In SHM, the acceleration (a) is directly proportional to the displacement (x) and is always directed towards the mean position. This can be mathematically expressed as: \[ a = -k x \] where \( k \) is a positive constant. 2. **Analyzing Each Given Option**: - We have four options for the relation between acceleration and displacement: 1. \( a_x = +2x \) 2. \( a_x = +2x^2 \) 3. \( a_x = -2x^2 \) 4. \( a_x = -2x \) 3. **Identifying the Correct Form**: - For SHM, we need \( a \) to be proportional to \( x \) with a negative sign. This means we are looking for a relation of the form \( a = -kx \). 4. **Evaluating Each Option**: - **Option 1**: \( a_x = +2x \) - This is positive and does not represent SHM. - **Option 2**: \( a_x = +2x^2 \) - This is also positive and not linear in x, hence does not represent SHM. - **Option 3**: \( a_x = -2x^2 \) - This is negative but not linear in x (it has \( x^2 \)), hence does not represent SHM. - **Option 4**: \( a_x = -2x \) - This is negative and linear in x, which matches the condition for SHM. 5. **Conclusion**: - The particle undergoing simple harmonic motion is described by the equation: \[ a_x = -2x \] Therefore, the correct answer is **Option 4**.
To determine which particle is undergoing simple harmonic motion (SHM) based on the given relations between acceleration (a) and displacement (x), we can analyze the provided equations step by step. ### Step-by-Step Solution: 1. **Understanding the Relation of Acceleration and Displacement**: - In SHM, the acceleration (a) is directly proportional to the displacement (x) and is always directed towards the mean position. This can be mathematically expressed as: \[ a = -k x ...
Promotional Banner

Similar Questions

Explore conceptually related problems

The ralation between acceleration and displacement of four particles are given below which one of the particles is executing simple harmonic motion?

The relation between acceleration and displacement of four partical are given below Which, one of the particle is exempting simple harmonic motion ?

Write the relation between acceleration, displacement and frequency of a particle executing SHM.

Which of the following relationships between the acceleration a and the displacement x of a particle executing simple harmonic motion?

The figure shows a graph between velocity and displacement (from mean position) of a particle performing SHM :

The displacement-time graph of a particle is as shown below. It indicates that

Draw the graph between displacement and potential energy for a particle executing SHM.

The graph between displacement and time for a particle moving with uniform acceleration is a

The velocity time relation of a particle is given by v = (3t^(2) -2t-1) m//s Calculate the position and acceleration of the particle when velocity of the particle is zero . Given the initial position of the particle is 5m .

Draw the graph between displacement and total energy for a particle executing SHM.