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Chapter 9: Q. 3 (page 227)

A mother has four times the mass of her young son. Both are running with the same kinetic energy. What is the ratio vson /vmother of their speeds?

Short Answer

Expert verified

The ratio of speed is vson /vmother = 2:1

Step by step solution

01

Given information

A mother has four times the mass of her young son.

Both are running with the same kinetic energy

02

Explanation

The kinetic energy is calculated by

KE = 1/2(mv2) .....................................(1)

Use equation (1) to calculate the kinetic energy of son and mother and find the ratio

Lets assume

Suppose K . Eson is the kinetic energy for son and

K . Emother is the kinetic energy for mother and it is given that both have same kinetic energy

K·Eson=K·Emother0.5×Mson×Vson=20.5×Mmother×Vmother2Mmother=4×MsonVson2/Vmother2=Mmother/MsonSubstitute the given valuesVson/Vmother2=4/1Take square root both sidesVson/Vmother=2/1=2:1

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