Answer
Verified
417.6k+ views
Hint: Calculate the distance covered in one revolution of the wheel. Hence calculate the total number of revolutions equivalent to 66kms. This will give the number of revolutions per hour. Hence calculate the number of revolutions in 10 mins. Alternatively, calculate the angular velocity of the wheel and hence the number of revolutions in 10mins.
Complete step-by-step answer:
The wheel covers a distance equal to the length of the circumference of the wheel in one revolution.
Given the diameter of the wheel = 80 cm =0.8 m
Hence the radius of the wheel = 0.4m.
Hence distance covered in one revolution $ =2\pi \left( 0.4 \right)=0.8\pi $ .
Hence the number of revolutions in 1 hour $ =\dfrac{66\times 1000}{0.8\pi }=\dfrac{66000\times 7}{0.8\times 22}=\dfrac{21000}{0.8}=26250 $ revolutions.
Hence the number of revolutions in 60 mins = 26250
Hence the number of revolutions in 1 min $ =\dfrac{26250}{60}=437.5 $
Hence the number of revolutions in 10 mins $ =437.5\times 10 $ = 4375 revolutions.
Hence option [c] is correct.
Note: The speed at the circumference of the wheel = 66km/h $ =\dfrac{66\times 1000}{60}\text{m/min=} $ 1100 m/min.
We know that angular velocity $ =\dfrac{\text{Velocity at point P}}{\text{Distance of point P from centre}} $
Hence, we have
Angular velocity $ =\dfrac{1100}{0.4}\text{rad}/\min =2750 $ rad/min
Since in a complete revolution we cover $ 2\pi $ radians, we have
The number of revolutions in 1 min $ =\dfrac{2750}{2\pi }=437.5 $
Hence the number of revolutions in 10 mins = 4375 revolutions.
Hence option [c] is correct.
Complete step-by-step answer:
The wheel covers a distance equal to the length of the circumference of the wheel in one revolution.
Given the diameter of the wheel = 80 cm =0.8 m
Hence the radius of the wheel = 0.4m.
Hence distance covered in one revolution $ =2\pi \left( 0.4 \right)=0.8\pi $ .
Hence the number of revolutions in 1 hour $ =\dfrac{66\times 1000}{0.8\pi }=\dfrac{66000\times 7}{0.8\times 22}=\dfrac{21000}{0.8}=26250 $ revolutions.
Hence the number of revolutions in 60 mins = 26250
Hence the number of revolutions in 1 min $ =\dfrac{26250}{60}=437.5 $
Hence the number of revolutions in 10 mins $ =437.5\times 10 $ = 4375 revolutions.
Hence option [c] is correct.
Note: The speed at the circumference of the wheel = 66km/h $ =\dfrac{66\times 1000}{60}\text{m/min=} $ 1100 m/min.
We know that angular velocity $ =\dfrac{\text{Velocity at point P}}{\text{Distance of point P from centre}} $
Hence, we have
Angular velocity $ =\dfrac{1100}{0.4}\text{rad}/\min =2750 $ rad/min
Since in a complete revolution we cover $ 2\pi $ radians, we have
The number of revolutions in 1 min $ =\dfrac{2750}{2\pi }=437.5 $
Hence the number of revolutions in 10 mins = 4375 revolutions.
Hence option [c] is correct.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Assertion CNG is a better fuel than petrol Reason It class 11 chemistry CBSE
How does pressure exerted by solid and a fluid differ class 8 physics CBSE
Number of valence electrons in Chlorine ion are a 16 class 11 chemistry CBSE
What are agricultural practices? Define
What does CNG stand for and why is it considered to class 10 chemistry CBSE
The rate of evaporation depends on a Surface area b class 9 chemistry CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
State whether the following statement is true or false class 11 physics CBSE
A night bird owl can see very well in the night but class 12 physics CBSE