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A particle is in linear simple harmonic motion between two points. $A$ and $B, 10 \mathrm{~cm}$ apart (figure.) take the direction from $A$ to $B$ as the positive direction and choose the correct statements.
$A O=O B=5 \mathrm{~cm}$
$B C=8 \mathrm{~cm}$
Options:
$A O=O B=5 \mathrm{~cm}$
$B C=8 \mathrm{~cm}$
- A
The sign of velocity, acceleration and force on the particle when it is $3 \mathrm{~cm}$ away from $A$ going towards $B$ are positive
- B
The sign of velocity of the particle at $C$ going towards $B$ is negative
- C
The sign of velocity, acceleration and force on the particle when it is $4 \mathrm{~cm}$ away from $B$ going towards $A$ are negative
- D
The sign of acceleration and force on the particle when it is at points $B$ is negative.
Solution:
2264 Upvotes
Verified Answer
The correct answers are:
The sign of velocity, acceleration and force on the particle when it is $3 \mathrm{~cm}$ away from $A$ going towards $B$ are positive
,
The sign of velocity, acceleration and force on the particle when it is $4 \mathrm{~cm}$ away from $B$ going towards $A$ are negative
,
The sign of acceleration and force on the particle when it is at points $B$ is negative.
The sign of velocity, acceleration and force on the particle when it is $3 \mathrm{~cm}$ away from $A$ going towards $B$ are positive
,
The sign of velocity, acceleration and force on the particle when it is $4 \mathrm{~cm}$ away from $B$ going towards $A$ are negative
,
The sign of acceleration and force on the particle when it is at points $B$ is negative.
Consider the diagram.
(a) When the particle is going from $A$ to $B$ (+ve direction) and the particle is $3 \mathrm{~cm}$ away from $A$ then velocity is towards $A B$ i.e. positive. Acceleration (in SHM) is always towards mean position $(O)$. So it is also positive.
(b) When the particle is at $C$, as the particle is going towards $(B)$, velocity is also towards $B$ hence velocity is positive not negative.
(c) When the particle is $4 \mathrm{~cm}$ away from $B$ going towards $A$ so velocity and acceleration both are towards mean position $(O)$. Hence both are negative.
(d) When the particle is at $B$, acceleration and force both are towards ' $O$ ', so that both are negative.
(a) When the particle is going from $A$ to $B$ (+ve direction) and the particle is $3 \mathrm{~cm}$ away from $A$ then velocity is towards $A B$ i.e. positive. Acceleration (in SHM) is always towards mean position $(O)$. So it is also positive.
(b) When the particle is at $C$, as the particle is going towards $(B)$, velocity is also towards $B$ hence velocity is positive not negative.
(c) When the particle is $4 \mathrm{~cm}$ away from $B$ going towards $A$ so velocity and acceleration both are towards mean position $(O)$. Hence both are negative.
(d) When the particle is at $B$, acceleration and force both are towards ' $O$ ', so that both are negative.
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