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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 \mu is large enough to help rolling motion)

Question

Angular acceleration of the ball after it has rotated through an angle \mathrm{\theta\left(\theta<180^{\circ}\right)}, is

Option: 1

\mathrm{\frac{5}{7} \frac{\pi \mathrm{niB}}{\mathrm{m}} \cos \theta}


Option: 2

\mathrm{\frac{2}{5} \frac{\pi n i B}{m} \cos \theta}


Option: 3

\mathrm{\frac{7}{5} \frac{\pi n i B}{m} \cos \theta}


Option: 4

\mathrm{\frac{5}{2} \frac{\pi \mathrm{niB}}{\mathrm{m}} \cos \theta}


Answers (1)

best_answer

\mathrm{\begin{aligned} & \mu \mathrm{B} \cos \theta-\mathrm{fr}=\mathrm{I} \alpha \\ & \mathrm{f}=\mathrm{ma}_{\mathrm{em}}=\mathrm{m} \mathrm{r} \alpha \\ & \alpha=\frac{5}{7} \pi \frac{\mathrm{niB}}{\mathrm{m}} \cos \theta \end{aligned}} 

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sudhir.kumar

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