The effective acceleration of a body, when thrown upwards with acceleration $a$ (in a frame moving with accele

Question

The effective acceleration of a body, when thrown upwards with acceleration $a$ (in a frame moving with acceleration $a$) will be:

Accepted Answer

1. **Analyze the Frame of Reference:** The problem describes a body being thrown upwards from a system (like a lift) that is accelerating with acceleration $a$. The phrase 'thrown upwards with acceleration a' typically implies the frame of reference is accelerating upwards with $a$.
2. **Effective Acceleration Concept:** In a non-inertial frame of reference (accelerating frame), a pseudo-force acts on the body in the direction opposite to the frame's acceleration. 
   - Acceleration of the frame = $a$ (upwards).
   - Acceleration due to gravity = $g$ (downwards).
   - Pseudo-acceleration acting on the body = $a$ (downwards, relative to the frame).
3. **Calculate Net Effective Acceleration:** The effective acceleration ($g_{eff}$) experienced by the body is the vector sum of gravity and the pseudo-acceleration.
   $$ \vec{g}_{eff} = \vec{g} + \vec{a}_{pseudo} $$
   Since both act downwards:
   $$ g_{eff} = g + a $$
   Therefore, the effective acceleration is $(g + a)$ or $(a + g)$ .
4. **Note on Answer Discrepancy:** The 'Probable Answer' provided in the input is $(a - g)$. This would be correct if the frame were accelerating *downwards* (where $g_{eff} = g - a$) or if $a$ referred to the net acceleration against gravity ($a_{net} = a_{applied} - g$). However, for the standard case of 'upward acceleration', $(a + g)$ is the physically correct effective acceleration.

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