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Question
In an imaginary atmosphere, the air exerts a small force F on any particle in the direction of the particle's motion. A particle of mass m projected upward takes time t1 in reaching the maximum height and t2 in the return journey to the original point. Then.
Options
t1 < t2
t1 > t2
t1 = t2
the relation between t1 and t2 depends on the mass of the particle
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Solution
t1 > t2
Let acceleration due to air resistance force be a.
Let H be maximum height attained by the particle.
Direction of air resistance force is in the direction of motion.
In the upward direction of motion,
\[a_{eff} = \left| g - a \right|\]
\[t_1 = \sqrt{\frac{2H}{\left| g - a \right|}} . . . (1)\]
In the downward direction of motion,
\[a_{eff} = g + a\]
\[t_2 = \sqrt{\frac{2H}{g + a}} . . . (2)\]
So, t1 > t2.
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