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KE of a body is increased by 44%. What is the percent increase in the momentum?10%20%30%44%

Question

KE of a body is increased by 44%. What is the percent increase in the momentum?10%20%30%44%

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Solution

The kinetic energy (KE) of an object is given by the formula KE = 1/2 mv^2, where m is the mass and v is the velocity (which is directly related to momentum).

If the kinetic energy is increased by 44%, we can express this as KE_new = 1.44 * KE_original.

We want to find the percent increase in momentum, which is given by p = mv.

Since the mass of the object doesn't change, we can say that the increase in kinetic energy is due to the increase in velocity.

So, we have:

1.44 * (1/2) m v^2 = (1/2) m (v_new)^2

Solving for v_new, we get:

v_new = sqrt(1.44) * v

The percent increase in velocity (and therefore momentum, since mass is constant) is then:

(sqrt(1.44) - 1) * 100% = 20%

So, the percent increase in the momentum is 20%.

This problem has been solved

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