An automobile moves on a road with a speed of 54 km h^-1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m² . If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its breaks to the wheel is

6.66 kg m²s^-2

8.58 kg m²s^-2

10.86 kg m²s^-2

2.86 kg m²s^-2

Solution

6.66 kg m²s^-2

As velocity of an automobile vehicle
$straight v space equals space 54 space km divided by straight h space equals space 54 space straight x space 5 over 18 space equals space 15 space straight m divided by straight s Angular space velocity space of space straight a space vehicle comma space straight v space equals space straight omega subscript straight o straight r rightwards double arrow space straight omega subscript straight o space equals space straight v over straight R space equals space fraction numerator 15 over denominator 0.45 end fraction space equals space 100 over 3 space rad divided by straight s So comma space angular space acceleration space of space an space antomobile straight alpha space equals space fraction numerator increment straight omega over denominator straight t end fraction space equals space fraction numerator straight omega subscript straight t minus straight omega subscript straight o over denominator straight t end fraction space equals space fraction numerator 0 minus begin display style 100 over 3 end style over denominator 15 end fraction space equals space fraction numerator negative 100 over denominator 45 end fraction space rad divided by straight s squared Thus comma space average space torque space transmitted space by space its space brakes space to space wheel torque space equals space Iα rightwards double arrow space 3 space straight x space 100 over 45 space equals space 6.66 space kg space straight m squared straight s to the power of negative 2 end exponent$

Some More Questions From Units and Measurement Chapter

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Units And Measurement

Some More Questions From Units and Measurement Chapter

What is the need of measurement?

Define physical quantity.

Give four examples of physical quantities.

Define unit.

What are the two main required characteristics of a unit?

Can we use same units for different physical quantities?

Can we use different units to measure same physical quantity?

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

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