A particle is in linear simple harmonic motion between two points `A` and `B 10cm` apart (figure). Take the direction form `A` to `B` as positive direction and choose the correct statements.
`AO =OB = 5cm`
`BC =8cm`

Options

A. The sign of velocity, acceleration 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 `B` is negative
C. The sign of velocity, acceleration 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

A, C, D

Explanation

In option (a): When the particle is `3cm` away form `A` going towards `B`. So, velocity is towards `AB`, i.e, position. In `SHM`, Acceleration is always towards mean position `(O)` it means both force and acceleration act towards `O`, have positive sign. Hence option (a) is correct. In option (b): When the particle is at `C`, velocity is towards `B` hence positive. Hence options (b) is not correct
In option (c ): When the particle is `4cm` away form `b` going towards `A` velocity is negative and acceleration is towards mean position `(O)`, hence negative. Hence option (c ) is correct. In option (d): Acceleration is always towards mean position `(O)`. When the particle is at `B`, acceleration and force are towards `BA` that is negative. Hence option (d) is correct.