Question

The particle is in linear simple harmonic motion between two points A and B ,$10cm$ apart.take the direction A to B as the positive direction and choose the correct statement.

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

Answer 1

Answer: (A), (D)

The correct options are
A The sign of acceleration,velocity and force on the particle when it is $3cm$ away from A going towards B are positive
D The sign of acceleration and force on the particle when it is at point B is negative

$M$ is the mean position of the linear $SHM$. (Motion is periodic along a straight line)

Velocity of the particle is maximum at centre & minimum at extreme positions.

(i) If the particle is $3cm$ away from $A$ & going towards $B$.

acc is $+ve$ $\Rightarrow$ force is $+ve$

vel. is $+ve$

(ii) If the particle is at pt $B$.

acc is $-ve$

$\Rightarrow$ force is also $-ve$

(iii) If particle is $4cm$ away from $B$ going towards $A$ then,

vel. is $+ve$

acc is $+ve$

$\Rightarrow$ force is also $+ve$

Hence Option (A) & (D) are correct.