Q. A bus moves over a straight level road with a constant acceleration $a$. A body in the bus drops a ball outside. The acceleration of the ball with respect to the bus and the earth are respectively
A) $a$ and $g$
B) $a + g$ and $g - a$
C) $\sqrt{a^{2} + g^{2}}\ $and $g$
D) $\sqrt{a^{2} + g^{2}}\ $and $a$
Explanation
(c) Let ${\overrightarrow{a}}_{rel}$ = acceleration of ball with respect to ground – acceleration of bus with respect to ground
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$= - g\widehat{j} - a\widehat{j}$
$\left| {\overrightarrow{a}}_{rel} \right| = \sqrt{g^{2} + a^{2}}$
Hence, (c) is correct.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.