Question

A car is moving in a circular path of diameter 100m with the vilocity of 10 m/sec . In how much time car will cover it path​

Answer 1

$\bigstar$ Answer

• Time to complete 1 revolution , t = 31.4 s

$\bigstar$ Given

• A car is moving in a circular path of diameter 100 m with the velocity of 10 m/sec

$\bigstar$ To Find

• Time to cover 1 revolution

$\bigstar$ Concept  Used

• Distance for 1 revolution of circular path = 2πr

$\bigstar$ Solution

Diameter , D = 100 m

We know that ,

Diameter , D = 2 × radius

⇒ D = 2r

⇒ 100 = 2r

⇒ r = 50 m

So , Radius , r = 50 m

Distance for 1 revolution , d = 2πr

⇒ d = 2π(50)

⇒ d = 100π

Velocity , v = 10 m/s

Time , t = ? s

We know that , " Velocity is defined as displacement per unit time "

$\rm \implies Velocity,v=\dfrac{Displacement,d}{Time,t}\\\\\implies \rm v=\dfrac{d}{t}\\\\\implies \rm 10=\dfrac{100 \pi}{t}\\\\\implies \rm t=\dfrac{100 \pi}{10}\\\\\implies \rm t=\dfrac{10 \pi}{1}\\\\\implies \rm t=10 \times 3.14\\\\\implies \rm t=31.4\ s$

Answer 2

$\bigstar$ $\sf{\green{\underline{\underline{\orange{To\:Find:-}}}}}$

• In How much time car will cover it's path .

$\bigstar$ $\sf{\blue{\underline{\underline{\purple{SOLUTION:-}}}}}$

☞ GIVEN :-

• Diameter (d) = 100 m

• Velocity (v) = 10 m/s

☞ Diameter = 2 × Radius

=> Radius (r) = 100/2 = 50 m

☞ Car moving in Circular path means Car moving in the perimeter of the circular path .

$\checkmark\:\tt{\underline{\boxed{\purple{Perimeter\:of\:Circle\:=\:2{\pi}r\:}}}}$

$\tt{\implies\:Perimeter\:=\:2{\pi}\times{50}\:}$

$\tt{\implies\:Perimeter\:=\:100{\pi}\:}$

☞ Thus, Car covered by $\tt{100{\pi}}$ distance .

☞ Now, we have know the relationship,

$\checkmark\:\tt{\underline{\boxed{\red{Velocity\:=\:{\dfrac{distance}{time}}\:}}}}$

$\tt{\implies\:time\:=\:{\dfrac{distance}{velocity}}\:}$

$\tt{\implies\:time\:=\:{\dfrac{100{\pi}}{10}}\:}$

$\tt{\implies\:time\:=\:10{\pi}\:}$

$\tt{\implies\:time\:=\:10\times{3.14}\:}$

$\tt{\boxed{\implies\:time\:=\:31.4\:second\:}}$