If the kinetic energy of a body increases by 800 %, its momentum increases by (a) 400 % (b) 200

step 1 we have problem number 142 in which it is given that if kinetic energy increases by 800 so momen

If the kinetic energy of a body increases by 800 %, its...

Key Concepts

Percentage Increase Calculation

A percentage increase expresses how much a quantity has grown relative to its initial value. When a quantity increases by a specified percent (for instance, an 800% increase implies the new value is nine times the original), the resulting percentage change in a related variable can be determined by applying the appropriate mathematical relationships, in this case, taking the square root to relate kinetic energy to momentum.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion. It is commonly expressed as KE = ½mv², demonstrating how energy depends on the mass and the square of the velocity. This quadratic dependence on velocity is crucial when comparing changes in kinetic energy to changes in momentum.

Momentum

Momentum is a measure of the quantity of motion of an object and is defined as the product of its mass and velocity (p = mv). Unlike kinetic energy, momentum is linearly proportional to velocity, which affects how proportional changes in kinetic energy translate into changes in momentum.

Relationship Between Kinetic Energy and Momentum

Since kinetic energy is proportional to the square of momentum (KE ? p²/(2m) for a given mass), any multiplicative change in kinetic energy results in a change in momentum by the square root of that factor. This mathematical relationship is essential in determining how an increase in kinetic energy affects momentum.

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