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  • Write–Up–II A person wants to roll a solid non-conducting spherical ball of mass m and radius r on a surface whose coefficient of static friction is <img alt="\m

Write–Up–II
A person wants to roll a solid non-conducting spherical ball of mass m and radius r on a surface whose coefficient of static friction is \mu. He placed the ball on the surface wrapped with n turns of closely packed conducting coils of negligible mass at the diameter. By some arrangement he is able to pass a current i through the coils either in the clockwise direction or in the anti-clockwise direction.

A constant horizontal magnetic field B is present throughout the space as shown in the figure. (Assume \vec{B} is large enough to help rolling motion)

Question

The minimum value of \mu for which the rolling motion is possible, is

 

Option: 1

\mathrm{\left(\frac{14 \pi}{5 g}\right)\left(\frac{\mathrm{niB}}{\mathrm{m}}\right) \mathrm{r}}


Option: 2

\mathrm{\left(\frac{5 \pi}{7 g}\right)\left(\frac{\mathrm{niB}}{\mathrm{m}}\right) \mathrm{r}}


Option: 3

0


Option: 4

\mathrm{\left(\frac{7 \pi}{5 g}\right)\left(\frac{\mathrm{niB}}{\mathrm{m}}\right) \mathrm{r}}


Answers (1)

best_answer

\mathrm{\begin{aligned} & \mathrm{f}=\mathrm{mr} \alpha \\ & \mu \mathrm{mg}=\mathrm{mr}\left(\frac{5}{7} \frac{\pi \mathrm{niB}}{\mathrm{m}}\right) \\ & \mu=\frac{5 \pi}{7 \mathrm{~g}}\left(\frac{\mathrm{niB}}{\mathrm{m}}\right) \mathrm{r} \end{aligned}}

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Rishi

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