Question

If the mass of the body is doubled what should be its speed so as to maintain the same kinetic energy ?​

Answer 1

Answer:

The speed should be reduced by 1/√2 or 0.707 times

Explanation:

The relationship between the kinetic energy, mass and velocity can be represented by the following equation:

K.E = ½m.v²

In this equation, the mass is inversely proportional to the square of the velocity or speed. This means that as the mass increases, the speed reduces by × 2.

Let; initial mass = m1

Final mass = m2

Initial velocity = v1

Final velocity = v2

According to the question, if the mass of the body is doubled i.e. m2 = 2m

½m1v1² = ½m2v2²

½ × m × v1² = ½ × 2m × v2²

Multiply both sides by 2

(½ × m × v1²)2 = (½ × 2m × v2²)2

m × v1² = 2m × v2²

Divide both sides by m

v1² = 2v2²

Divide both sides by 2

v1²/2= v2²

Square root both sides

√v1²/2= √v2²

v1/√2 = v2

v2 = 1/√2 v1

This shows that to maintain the same kinetic energy if the mass is doubled, the speed should be reduced by 1/√2 or 0.707 times.