Dynamics of Circular Motion

Practice Questions:

Question 11: easy

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)

1. √19 m/s

2. √29 m/s

3. √39 m/s

4. √49 m/s

View Answer

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 12: easy

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

1. π/4

2. π/3

3. π/6

4. π/2

View Answer

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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