Kinetic energy of a body decreases by 19%. What is the percentage decrease in linear momentum?

(A) 15%

(B) 5%

(C) 20%

(D) 10%

To determine the percentage decrease in linear momentum when the kinetic energy of a body decreases by 19%, we need to understand the relationship between kinetic energy and momentum. Kinetic energy (KE) is given by the formula:

Kinetic Energy and Momentum Formulas

The kinetic energy of an object is defined as:

KE = (1/2) mv²

where m is the mass and v is the velocity. The momentum (p) of an object is defined as:

p = mv

Relationship Between Kinetic Energy and Momentum

From these formulas, we can derive the relationship between kinetic energy and momentum. If we express kinetic energy in terms of momentum, we can rearrange the equations:

Since p = mv, we can express v as v = p/m. Substituting this into the kinetic energy formula, we get:

KE = (1/2) m (p/m)² = (p²)/(2m)

Analyzing the Percentage Decrease

Now, let's denote the initial kinetic energy as KE₀ and the initial momentum as p₀. If the kinetic energy decreases by 19%, the new kinetic energy KE₁ can be expressed as:

KE₁ = KE₀ - 0.19 KE₀ = 0.81 KE₀

Substituting into our derived formula, we have:

0.81 KE₀ = (p₁²)/(2m)

Since KE₀ = (p₀²)/(2m), we can substitute this into the equation:

0.81 (p₀²)/(2m) = (p₁²)/(2m)

This simplifies to:

0.81 p₀² = p₁²

Finding the New Momentum

Taking the square root of both sides, we get:

p₁ = p₀ √0.81 = p₀ × 0.9

This indicates that the new momentum is 90% of the original momentum, which means there is a decrease of:

Δp = p₀ - p₁ = p₀ - 0.9 p₀ = 0.1 p₀

Calculating the Percentage Decrease

To find the percentage decrease in momentum, we can express it as:

Percentage decrease = (Δp / p₀) × 100%

Substituting the values gives us:

Percentage decrease = (0.1 p₀ / p₀) × 100% = 10%

Thus, the percentage decrease in linear momentum is 10%. Therefore, the correct answer to your question is (D) 10%.

simply answer is 10%