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 t_{1} in reaching the maximum height and t_{2} in the return journey to the original point. Then.

#### Options

t

_{1}< t_{2}t

_{1}> t_{2}t

_{1}= t_{2}the relation between t

_{1}and t_{2}depends on the mass of the particle

#### Solution

t_{1} > t_{2}

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, t_{1} > t_{2}.