Physics - NLM Question with Solution | TestHub

Let $T_1$ be the tension between $m$ and the insect, $T_2$ between the insect and the person. The insect has acceleration $a-a_0$ relative to the ground (string moves with $a$, insect moves back at $a_0$ relative to string, so its acceleration is $a_0-a$ in the direction of $T_1$).

Insect: $T_1-T_2=m^{\prime }(a_0-a)$ ... (1). Block: $T_1=ma$ ... (2).

From (1),(2): $T_2=ma-m^{\prime }(a_0-a)=ma+m^{\prime }(a-a_0)$.

$\frac{T_1}{T_2}=\frac{ma}{ma+m^{\prime }(a-a_0)}$.