A solid metallic sphere of radius r is allowe | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

The frictional resistance $f_{r}$ is given as$:$

$f_{r} \propto A$ and $f_{r} \propto v^{2}$

$f_{r}=k A v^{2}(	ext { here } \mathrm{k}$ is a co

Vedclass · Accepted Answer

$r^{1/2}$

Vedclass · Answer

The frictional resistance $f_{r}$ is given as$:$

$f_{r} \propto A$ and $f_{r} \propto v^{2}$

$f_{r}=k A v^{2}(	ext { here } \mathrm{k}$ is a constant)

The downwards force is given as$:$ $m g=\frac{4}{3} \pi r^{3} ho g$

Balancing the above we get the terminal velocity as$:$

$\frac{4}{3} \pi r^{3} ho g=k\left(\pi r^{2}ight) v^{2}$

$r \propto v^{2}$

$v \propto r^{1 / 2}$

A solid metallic sphere of radius $r$ is allowed to fall freely through air. If the frictional resistance due to air is proportional to the cross-sectional area and to the square of the velocity, then the terminal velocity of the sphere is proportional to which of the following?

Similar Questions

Write $\mathrm{SI}$ and $\mathrm{CGS}$ unit of coefficient of viscosity.

Write one of the practical use of viscosity.

Which falls faster, big rain drops or small rain drops ?

A copper ball of radius $'r'$ travels with a uniform speed $'v'$ in a viscous fluid. If the ball is changed with another ball of radius $'2r'$ , then new uniform speed will be

$Assertion :$ Falling raindrops acquire a terminal velocity.
$Reason :$ A constant force in the direction of motion and a velocity dependent force opposite to the direction of motion, always result in the acquisition of terminal velocity.