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A block of mass m is projected on a smooth horizontal circular track with a velocity v. What is the average normal force (define it as mass multiplied with average acceleration) exerted by the circular walls on the block during its motion form A to B?

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$\frac{m v^{2}}{2 π R}$

$\frac{m v^{2}}{π R}$

$\frac{2 m v^{2}}{R}$

$\frac{2 m v^{2}}{π R}$

answer is D.

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Detailed Solution

$< a > = \frac{Δ v}{Δ t} = \frac{v (\leftarrow) - v (\to)}{\frac{π R}{v}} = \frac{2 v^{2}}{π R} (\leftarrow)$

$∴ < F > = \frac{2 m v^{2}}{π R} (\leftarrow)$

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