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Question

A car covers 90 km in 60 min, and a truck covers 54 km in the same period of time. The linear momentum of the truck is 15 × 103 kg m/s. The mass of the car is 500 kg.

The ratio of the kinetic energy of the car to the kinetic energy of the truck is:

[1 mark]

A
25:18
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B
5:9
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C
18:25
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D
9:5
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Solution

The correct option is A 25:18
Given,
Speed of the car = 90 km/hr = 25 m/s
Speed of the truck = 54 km/hr = 15 m/s
Mass of the car = 500 kg
Linear momentum of the truck = 15,000 kg m/s

For the truck:
Kinetic energy,
K.E. = 12mv2
K.E. = 12×1000×152
K.E. = 1,12,500 J

For the car:
Kinetic energy,
K.E. = 12mv2
K.E. = 12×500×252K.E. = 1,56,250 J

The ratio of the kinetic energy of the car to that of the truck = K.E.cK.E.t = 1,56,2501,12,500 = 2518

Where K.E.c = Kinetic energy of the car
and K.E.t = Kinetic energy of the truck

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