A block of 200 g mass moves with a uniform speed in a horizontal circular groove,
Question:

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

1. 0.0314 N

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

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

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

Correct Option: , 4

Solution:

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

$\mathrm{N}=\mathrm{m}\left[\frac{4 \pi^{2}}{\mathrm{~T}^{2}}\right] \mathrm{R}$       …..(1)

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

Put values in equation (1)

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