A block 200g mass moves with a uniform speed

Question:

A block of $200 \mathrm{~g}$ mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius $20 \mathrm{~cm}$. If the block takes $40 \mathrm{~s}$ to complete one round, the normal force by the side walls of the groove is:

  1. (1) $0.0314 \mathrm{~N}$

  2. (2) $9.859 \times 10^{-2} \mathrm{~N}$

  3. (3) $6.28 \times 10^{-3} \mathrm{~N}$

  4. (4) $9.859 \times 10^{-4} \mathrm{~N}$


Correct Option: , 4

Solution:

(4)

$\mathrm{N}=\mathrm{m} \omega^{2} \mathrm{R}$

$\mathrm{N}=\mathrm{m}\left[\frac{4 \pi^{2}}{\mathrm{~T}^{2}}\right] \mathrm{R}$

Given $\mathrm{m}=0.2 \mathrm{~kg}, \mathrm{~T}=40 \mathrm{~S}, \mathrm{R}=0.2 \mathrm{~m}$

Put values in equation (1)

$\mathrm{N}=9.859 \times 10^{-4} \mathrm{~N}$

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