Question

The wheel of a motor cycle is
of radius 35 cm. How many
revolutions per minute must
the wheel make so as to keep aspeed of 66 km/h?
300
O 400
450
500​

Answer 1

Answer :-

$\:\\\large{\boxed{\sf{Firstly,\;let's\;understand\;the\;concept\;used\;:-}}}$

Here the concept of Perimeter of Circle has been used. When we find out the circumference of the circle, then we can divide the speed given by uts circumference to find out the number of revolutions.

Let's do it !!

_________________________________________________

★ Formula Used :-

$\:\\\large{\boxed{\sf{Circumference\;of\;Circle\;\:=\;\:\bf{2 \pi r}}}}$

$\:\\\large{\boxed{\sf{66\;\;Km\:hr^{-1}\;\:=\;\:\bf{\dfrac{66\:\times\:1000}{60}\;\;m\:min^{-1}}}}}$

$\:\\\large{\boxed{\sf{Number\;of\;Revolutions\;\:=\;\:\bf{\dfrac{Distance\;covered\;in\;one\;minute}{Circumference\;of\;circle}}}}}$

_________________________________________________

★ Question :-

The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/h ?

_________________________________________________

★ Solution :-

Given,

» Radius of wheel = r = 35 cm = 0.35 m

» Speed attained = 66 Km/hr

_________________________________________________

~ For the Speed Attained in m/min :-

$\:\\\qquad\large{\sf{:\longrightarrow\;\;\:66\;\;Km\:hr^{-1}\;\:=\;\:\bf{\dfrac{66\:\times\:1000}{60}\;\;m\:min^{-1}\;\:=\;\;\underline{\underline{1100\;\;m\:min^{-1}}}}}}$

$\:\\\large{\boxed{\boxed{\tt{Speed\;\;attained\;\;by\;\;Wheel\;\;=\;\bf{1100\;\;m\:min^{-1}}}}}}$

This is the distance covered by wheel in 1 minute.

_________________________________________________

~ For the Circumference of the Wheel :-

$\:\\\qquad\large{\sf{:\longrightarrow\;\;\:Circumference\;of\;Circle_{(wheel)}\;\:=\;\:\bf{2 \pi r}}}$

$\:\\\qquad\large{\sf{:\longrightarrow\;\;\:Circumference\;of\;Circle_{(wheel)}\;\:=\;\:\bf{2\:\times\:\dfrac{22}{7}\:\times\:0.35\;\:=\;\:\underline{\underline{2.2\;\;m}}}}}$

$\:\\\large{\boxed{\boxed{\tt{Circumference\;\;of\;\;Wheel\;\;=\;\bf{2.2\;\;m}}}}}$

This is the distance covered by wheel in 1 revolution.

_________________________________________________

To find the answer, we need to simply divide, distance covered in 1 min by distance covered in 1 revolution.

$\:\\\qquad\large{\sf{:\Longrightarrow\;\;\:Number\;of\;Revolutions\;\:=\;\:\bf{\dfrac{Distance\;covered\;in\;one\;minute}{Circumference\;of\;circle}}}}$

$\:\\\qquad\large{\sf{:\Longrightarrow\;\;\:Number\;of\;Revolutions\;\:=\;\:\bf{\dfrac{1100}{2.2}\:\;=\;\:\underline{\underline{500\;\;revolutions}}}}}$

So the correct answer is :-

Option D.) 500 Revolutions.

$\:\\\large{\underline{\underline{\rm{Thus,\;number\;of\;revolutions\;made\;by\;wheeel\;are\;\;\boxed{\bf{500\;\;revolutions}}}}}}$

_________________________________________________

$\:\\\large{\underbrace{\mapsto\;\;\:More\;to\;know\;:-}}$

$\:\\\sf{\leadsto\;\;Area\;of\;Square\;=\;(Side)^{2}}$

$\:\\\sf{\leadsto\;\;Area\;of\;Rectangle\;=\;Length\:\times\:Breadth}$

$\:\\\sf{\leadsto\;\;Area\;of\;Parallelogram\;=\;Base\:\times\:Height}$

$\:\\\sf{\leadsto\;\;Area\;of\;Rectangle\;=\;\dfrac{1}{2}\:\times\:Base\:\times\:Height}$

$\:\\\sf{\leadsto\;\;Perimeter\;of\;Square\;=\;4\:\times\:Side}$

$\:\\\sf{\leadsto\;\;Area\;of\;Circle\;=\;\pi r^{2}}$

$\:\\\sf{\leadsto\;\;Perimeter\;of\;Rectangle\;=\;2\:\times\:(Length\:+\:Breadth)}$

Answer 2

Given,

The wheel of a motor cycle is  of radius 35 cm.

To find :

How many  revolutions per minute must  the wheel make so as to keep a speed of 66 km/h?

Solution :

Radius of wheel = 35 cm = 35/100 = 0.35 m

Speed which must be kept = 66km/h = (66 * 1000)/60 m/min

                                                               = 66000/60 m/min

                                                               = 1100 m/min

∴ Wheel covers 1100 m in 1 minute.

∴ Distance covered, d = 1100 m

Now, circumference of wheel :

⇒ Circumference = 2πr

⇒ Circumference = 2 * 22/7 * 0.35

⇒ Circumference = 15.4/7

⇒ Circumference = 2.2 m

Now number of revolutions :

⇒ Number of revolutions = Distance covered/Circumference

⇒ Number of revolutions = 1100/2.2

⇒ Number of revolutions = 500

Therefore,

The wheel must keep 500 revolutions per minute so as to keep a speed of 66 km/h.         [Option D]