Question

A rail-road car is moving towards the right with acceleration $a$ and a dog of mass $m$ is chasing a man $\left(A\right)$ with an acceleration $\frac{a}{3}$ relative to the car and the man $\left(A\right)$ is accelerating towards left with an acceleration of magnitude $\frac{a}{3}$ with respect to the car as shown in the figure. If an observer $B$ on the ground is observing both the dog and man $\left(A\right)$, then the net force experienced by the dog as seen by observer $B$ is

• A. $\frac{ma}{3}\hat{i}$
• B. $\frac{-ma}{3}\hat{i}$
• C. $\frac{-2ma}{3}\hat{i}$
• D. $\frac{2ma}{3}\hat{i}$

Answer 1

The correct option is D $\frac{2ma}{3}\hat{i}$

In the ground frame of observer $B$, considering acceleration of the car in positive $x-\text{axis}$, acceleration of dog w.r.t ground,
${\overrightarrow{a}}_{\text{dog, ground}}$=${\overrightarrow{a}}_{\text{dog, car}}$+${\overrightarrow{a}}_{\text{car, ground}}$
$=-\frac{a}{3}\hat{i}+a\hat{i}$
$=+\frac{2a}{3}\hat{i}$
Therefore, force experienced by dog w.r.t observer B on ground,
$\Rightarrow {\overrightarrow{F}}_{\text{dog, ground}}=m_{dog}{\overrightarrow{a}}_{\text{dog,ground}}=\frac{2ma}{3}\hat{i}$