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 from Physics System of Particles and Rotational Motion Class 11 Manipur Board
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System of Particles and Rotational Motion

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Physics Part I

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Physics

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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


A.

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

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

1932 Views

Define centre of mass.

Centre of mass of a body or a system of bodies is a point at which the entire mass of the body or system is supposed to be concentrated. 
1449 Views

Is it necessary that there should be matter at the centre of mass of system?

No, it is not necessary that there be matter at the centre of mass of the system.

For e.g., if two equal point masses are separated by certain distance, the centre of mass lies at the mid point of two point masses and there is no mass at that point.
730 Views

What is the need of centre of mass?

Newton’s second law of motion is strictly applicable to point masses only. To apply the Newton's law of motion to rigid bodies, the concept of centre of mass is introduced.

The concept of centre of mass of a system enables us to discuss overall motion of the system by replacing the system by an equivalent single point object. 
911 Views

Is it necessary for centre of mass to lie within the body?

No, centre of mass needs not to lie within the body. It is not necessary that the total mass of the system be actually present at the centre.

The position of the centre of mass is calculated using the usual Newtonian type of equations of motion. 
943 Views

What is the significance of defining the center of mass of a system?

The motion of n particle system can be reduced to one particle motion.

An equivalent single point object would enable us to discuss the overall motion of the system. 
794 Views