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.

विकल्प

• t₁ < t₂

•  t₁ > t₂

• t₁ = t₂

• the relation between t₁ and t₂ depends on the mass of the particle

Answer 1

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.