Dynamics of Circular Motion – Page 2 – Rankers Physics

Dynamics of Circular Motion

Question 1:
The maximum speed of car with which it can go around a level road of radius 10 m is (coefficient of friction between the road and tyre is 0.5)
(g = 9.8 m/s²)

√19 m/s

√29 m/s

√39 m/s

√49 m/s

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Solution:

The maximum speed on a level road is limited by static friction: u=v²/rg

Given μs=0.5, g=9.8m/s², and r=10m.

Substituting these values: V²max=(0.5)(9.8)(10)= 49 = 7m/s.

Therefore, the maximum speed is 7 m/s.

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Question 2:
A cyclist paddling at a speed of 10 m/s on a level road takes a sharp circular turn of radius 10 m without reducing the speed. The angle made by cyclist with vertical is

π/4

π/3

π/6

π/2

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Solution:

Using the formula $\tan \theta = \frac{v^2}{r g}$ and given values $v = 10$ m/s, $r = 10$ m, and $g = 10$ m/s², we get:

$\tan \theta = \frac{10^2}{10 \times 10} = 1$

Thus, $\theta = \tan^{-1}(1) = 45^\circ$ . The cyclist leans at 45° or π/4 with the vertical.

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