Question

A person walks around a circular track of radius
10 m with constant speed of 1 m's. The angle
traced by him with centre in 8 sec. is
​

Answer 1

Given :-

• Radius of circular track , r = 10 m
• speed of person , s = 1 ms⁻¹
• time for which person walks , t = 8 sec

To find :-

• Angle traced by Person with centre by walking for 8 sec.

Knowledge required :-

• Relation b/w speed , distance and time

$\orange{\bigstar}\boxed{\sf{distance=speed\times time}}$

• Relation b/w Angle θ (in radians) , radius r and length of arc l

$\orange{\bigstar}\boxed{\sf{\theta=\dfrac{l}{r}}}$

Solution :-

_________________________________

$\setlength{\unitlength}{5mm}\begin{picture}(6,6) \thicklines\put(0,0){\line(1,1){4}} \put(0,0){\line(-1,1){4}}\qbezier(-4,4))(0,6)(4,4) \put(0,-1){\bf{O}}\put(-4.8,4){\bf{A}} \put(4.6,4){\bf{B}} \qbezier(-0.5,0.5)( 0,1)(0.5,0.5)\put(0,1.5){ \theta }\put(3,1.5){\bf{r=10\;m}} \put(0,5.5){\bf{l}} \end{picture}$

• OB = r = 10 m is radius of circular track
• Arc AB = l is distance covered by Person
• θ is the angle (in radians) traced by him at centre

_________________________________

Calculating distance travelled by person

Using formula

$\implies\sf{distance=speed\times time }\\\\\implies\sf{distance \:travelled, l = 1 \times 8 }\\\\\underline{\underline{\implies\sf{distance\:travelled,l=8\;m}}}$

Calculating Angle traced by man at centre

Using formula

$\implies\sf{\theta=\dfrac{l}{r}}\\\\\implies\sf{\theta=\dfrac{8}{10}}\\\\\implies\underbrace{\underline{\underline{\boxed{\sf{\theta=\dfrac{4}{5}\;rad}}}}}\red{\bigstar}$

Hence,  

The correct option is

$\large{\red{\bf{\dfrac{4}{5}\;rad\;\;.}}}$