91Ó°ÊÓ

Viscosity of the liquid, $\mathrm{η}=1×{10}^{−3}\mathrm{Ns}/{\mathrm{m}}^2$.

The propulsion force is calculated as:

$F=6\mathrm{π}\mathrm{η}Rv$.

Here,

$R$is the diameter.

$\mathrm{η}$is the viscosity.

$v$is the velocity.

Propulsion force for the sphere of diameter $d=100\mathrm{μ}\mathrm{m}$swimming with the speed of $1\mathrm{mm}/\mathrm{s}$is calculated as,

$F=6\mathrm{π}\mathrm{η}Rv$

Plugging the values in the above equation

$\begin{array}{c}F=6\mathrm{π}×1×{10}^{−3}×\frac{100×{10}^{−6}}{2}×1×{10}^{−3}\\ =9.4×{10}^{−10}\mathrm{N}\end{array}$

Propulsion force of $2\mathrm{μ}\mathrm{m}$diameter coil swimming at $30\mathrm{μ}\mathrm{m}/\mathrm{s}$is calculated as:

$F=6\mathrm{π}\mathrm{η}Rv$

Plugging the values in the above equation:

$\begin{array}{c}F=6\mathrm{π}×1×{10}^{−3}×\frac{2×{10}^{−6}}{2}×30×{10}^{−6}\\ =5.7×{10}^{−13}\mathrm{N}\end{array}$

Density of the liquid,$\mathrm{ÒÏ}=1×{10}^3\mathrm{kg}/{\mathrm{m}}^3.$

The acceleration of the orgasm is calculated by the formula

$F=\mathrm{ÒÏ}Va$

Here,

$\mathrm{ÒÏ}$is the density

$V$is the volume

$a$is the acceleration

Acceleration of the orgasm for the propulsion force for the sphere of diameter $d=100\mathrm{μ}\mathrm{m}$swimming with the speed of $1\mathrm{mm}/\mathrm{s}$is calculated as:

$F=\mathrm{ÒÏ}Va$

Plugging the values in the above equation

$9.4×{10}^{−10}=1000×\frac{4}{3}×\mathrm{π}×{\left(\frac{100×{10}^{−6}}{2}\right)}^{3}a$.

$a=1.8\mathrm{m}/{\mathrm{s}}^2$.

Acceleration of the orgasm for the propulsion force o$2\mathrm{μ}\mathrm{m}$diameter coil swimming at$30\mathrm{μ}\mathrm{m}/\mathrm{s}$is calculated

as,

the speed of $1\mathrm{mm}/\mathrm{s}$is calculated as:

$F=\mathrm{ÒÏ}Va$

Plugging the values in the above equation

$9.4×{10}^{−10}=1000×\frac{4}{3}×\mathrm{π}×{\left(\frac{100×{10}^{−6}}{2}\right)}^{3}a$.

$a=1.8\mathrm{m}/{\mathrm{s}}^2$

$5.7×{10}^{−13}=1000×\frac{4}{3}×\mathrm{π}×{\left(\frac{2×{10}^{−6}}{2}\right)}^{3}a$

$a=130\mathrm{m}/{\mathrm{s}}^2.$

Part (a):

• Propulsion force for the sphere of diameter $d=100\mathrm{μ}\mathrm{m}$swimming with the speed of $1\mathrm{mm}/\mathrm{s}$is $9.4×{10}^{−10}\mathrm{N}$.
• Propulsion force of $2\mathrm{μ}\mathrm{m}$diameter coil swimming at $30\mathrm{μ}\mathrm{m}/\mathrm{s}$is$5.7×{10}^{−13}\mathrm{N}$.

Part (b):

• - Acceleration of the orgasm for the propulsion force for the sphere of diameter $d=100\mathrm{μ}\mathrm{m}$simming with the speed of $1\mathrm{mm}/\mathrm{s}$is $1.8\mathrm{m}/{\mathrm{s}}^2$.
• Acceleration of the orgasm for the propulsion force of $2\mathrm{μ}\mathrm{m}$diameter coil swimming at $30\mathrm{μ}\mathrm{m}/\mathrm{s}$is$130\mathrm{m}/{\mathrm{s}}^2$.