Question

A block of mass m is projected on a smooth horizontal circular track with velocity v. What is the average normal force exerted by the circular walls on the block during its motion from A to B?

• A. $\frac{m{v}^2}{R}$
• B. $\frac{m{v}^2}{\pi R}$
• C. $\frac{2m{v}^2}{R}$
• D. $\frac{2m{v}^2}{\pi R}$

Answer 1

The correct option is D $\frac{2m{v}^2}{\pi R}$

correct answer is D.

average acceleration ${\overrightarrow{a}}_{ave}=\frac{{\overrightarrow{V}}_f-{\overrightarrow{V}}_i}{\Delta t}$

=$\frac{v(-\hat{i})-v\hat{i}}{\delta t}$

=$\frac{-2v\hat{i}}{\delta t}$

time taken from A and B is

$\delta t=\frac{distance}{speed}$

=$\frac{\pi R}{v}$

${\overrightarrow{a}}_{ave}=\frac{-2v\hat{i}}{\frac{\pi R}{v}}=\left(\frac{-2v^2}{\pi R}\right)$

$force=m\times a$

=$m\times \frac{2v^2}{\pi R}$

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