Question

Two identical particles A and B, each of mass m, are interconnected by a spring of stiffness k. If particle B experiences a force F and the elongation of the spring is x, the acceleration of particle B relative to particle A is equal to

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Equation of motion for A (Fig),

Kx = ma $\Rightarrow a=\frac{kx}{m}$

For B:F - T = ma'

$\Rightarrow a^{\prime }=\frac{F-kx}{m}$

Thus, relative acceleration = $a_r=|a^{\prime }-a|=\frac{F-2kx}{m}$