A ball falls vertically downward and bounces off a horizontal floor. The speed of the ball just before reaching the floor $\left(\mathrm{u}_{1}\right)$ is equal to the speed just after having contact with the floor $\left(\mathrm{u}_{2}\right) ; \mathrm{u}_{1}=\mathrm{u}_{2} .$ The corresponding magnitudes of accelerations are denoted respectively by $a_{1}$ and $a_{2} .$ The air resistance during motion is proportional to speed and is not negligible. If $g$ is acceleration due to gravity, then-

• Correct answer
  A

  $a_{1} < a_{2}$
• B

  $a_{1}>a_{2}$
• C

  $\mathrm{a}_{1}=\mathrm{a}_{2} \neq \mathrm{g}$
• D

  $\mathrm{a}_{1}=\mathrm{a}_{2}=\mathrm{g}$

Solution

Downward- $a_{1}=g-\frac{F_{R}}{m}$ Upward:- $\quad a_{2}=g+\frac{F_{R}}{m}$ $\mathrm{a}_{2} < \mathrm{a}_{1}$

Hence, the correct answer is option: 'A'.