Question

A motorcycle is traveling on a curved track of radius 500 m. If the coefficient of friction between road and tyres is 0.5, the speed avoiding skidding will be

(A) 50 m/s
(B) 75 m/s
(C) 25 m/s
(D) 35 m/s

Answer 1

Hint:Start with finding the relation between the speed of the motorcycle, radius of the curved surface, frictional coefficient and the acceleration due to gravity applied on the motorcycle. Then after finding the relation put all the values from the information provided in the question and we will get the required answer.



Formula used:
Velocity, $v = \sqrt {\mu rg} $
Where, $\mu $ is frictional coefficient.
R is radius of the curved track.
And g is the acceleration due to gravity.


Complete answer:
Let start with the given information from the question:
Radius of the circular track is given as 500 m.
Coefficient of friction between the road and the tyres of the motorcycle is given as 0.5.
We know that acceleration due to gravity , g=10 m per sec square.
Now, for finding the speed of the motorcycle avoiding skidding we will use the following formula for the speed:
$v = \sqrt {\mu rg} $
Putting all the values here in the formula, we get;
$v = \sqrt {0.5 \times 500 \times 10} $
By solving, we get;
$v = 50m/s$

Hence, the correct answer is Option(A).

Note: Use the relation of velocity, radius of the curved track and the acceleration due to gravity and find the required answer but be careful about all the units being given of all the quantities and then only use them in the required formula and hence get the required answer for the same.