A particle of mass $m$ is moving with an acceleration $a / 3$ towards left relative to the trolley car. An observer accelerates towards left with an acceleration of magnitude $a / 3$ . The trolley moves towards right with an acceleration $a$ . Force experienced by particle ( in ground frame of reference) is $\frac{x m a}{3} (+ \hat{i})$ . The value of ‘ $x$ ’ is

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Detailed Solution

w.r.t ground, for particle

$\bar{F} = m \bar{a}_{p a r t i c l e}$

$= m ({\bar{a}}_{r e l} + {\bar{a}}_{t r o l l e y})$

$= m (- \frac{a}{3} \hat{i} + a \hat{i})$

$\bar{F} = \frac{2 m a}{3} \hat{i}$

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