Question

A solid sphere falls with a terminal velocity of $20{\text{ms}}^{-1}$ in air. If it is allowed to fall in vacuum,

• A. Terminal velocity will be $20{\text{ms}}^{-1}$.
• B. Terminal velocity will be less than $20{\text{ms}}^{-1}$.
• C. Terminal velocity will be more than $20{\text{ms}}^{-1}$.
• D. There will be no terminal velocity.

Answer 1

The correct option is D There will be no terminal velocity.

In air, terminal velocity is obtained when the net downward force (force due to gravity) becomes equal to net upward force (buoyancy and drag force)
i.e $W=F_v+F_B$
But in vaccum, there is no material medium. Hence, there will no resistance to the motion of the body. In case of air (fluid), due to slipping between the fluid layer and solid body, a drag force$\left(F_v\right)$ acts on the body.

Therefore in vacuum, only force acting is gravitational force on the body. Hence, it's an accelerated motion. Terminal velocity will be never attained.