Question

A particle is in linear simple harmonic motion between two points $\text{A}$ and $\text{B}$, which are $10\text{cm}$ apart as shown in the figure. Taking the direction from $\text{A}$ to $\text{B}$ as positive, choose the correct statement(s):
Given : $AO=OB=5\text{cm}$ , $BC=8\text{cm}$

• A. The signs of velocity, acceleration and force on the particle when it is $3\text{cm}$ away from $\text{A}$ going towards $\text{B}$ are positive.
• B. The sign of velocity of the particle at $C$ going towards $B$ is negative.
• C. The signs of velocity, acceleration and force on the particle when it is $4\text{cm}$ away from $B$ going towards $A$ are negative.
• D. The signs of acceleration and force on the particle when it is at point $B$ are negative.

Answer 1

Answer: (A), (C), (D)

The correct options are
A The signs of velocity, acceleration and force on the particle when it is $3\text{cm}$ away from $\text{A}$ going towards $\text{B}$ are positive.
C The signs of velocity, acceleration and force on the particle when it is $4\text{cm}$ away from $B$ going towards $A$ are negative.
D The signs of acceleration and force on the particle when it is at point $B$ are negative.

Consider the diagram.


When the particle is $3\text{cm}$ away from $\text{A}$ going towards $\text{B}$, velocity is positive.
Since the particle is moving towards the mean position along $\text{AB}$, acceleration is positive.
Thus, the force acting on the particle is also positive.
Hence, option (a) is correct.
(b) When the particle is at $C$, velocity is directed towards $B$, hence it is positive.
So, option (b) is wrong.
(c) When the particle is $4\text{cm}$ away from $B$ going towards $A$, velocity is negative and as acceleration is towards mean position $\left(O\right)$ along $\text{BA}$, acceleration is negative. Thus, force is also negative.
Hence, option (c) is correct.
(d) Acceleration is always towards mean position $\left(O\right)$. When the particle is at $B$, acceleration and force are towards mean position along $BA$. So, both are negative.
Thus, option (d) is also correct.