Question

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

• A. $6.28\times {10}^{-3}N$
• B. $0.0314N$
• C. $9.859\times {10}^{-2}N$
• D. $9.859\times {10}^{-4}N$

Answer 1

The correct option is D

$9.859\times {10}^{-4}N$

Step 1: Given data

Mass of a block, $m=200g=0.2Kg$

Radius of a sidewall, $R=20cm=0.2m$

Time taken to complete one round, $T=40s$

Step 2: Calculating the normal force

The angular velocity, $\omega =\frac{2\pi }{T}=\frac{2\times 3.14}{40}=0.157\raisebox{1ex}{$rad$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

The formula to calculate the normal force is:

$$\begin{gathered} N=m{\omega }^{2}R \\ \Rightarrow N=0.2\times {(0.157)}^2\times 0.2 \\ \Rightarrow N=9.8596\times {10}^{-4}Newton \end{gathered}$$

Hence, option(D) is the correct answer.