If kinetic energy of a body is increased by 300% then percentage change in momentum will be
Momentum is the quantity of motion possessed by a moving body, determined by the product of its mass and velocity. It is a vector quantity with both magnitude and direction and is conserved in isolated systems during collisions or interactions, playing a vital role in analyzing motion and forces.
Class 11 Physics Chapter 5 focuses on the concepts of work, energy and power. It covers definitions principles and relationships between these topics. Understanding these concepts is essential for analyzing mechanical systems and solving problems related to energy transformations and conservation in various physical situations in preparation for exams.
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To calculate the percentage change in momentum when the kinetic energy increases by 300%, let’s use the relationship between kinetic energy and momentum.
Step 1: Relationship between kinetic energy and momentum
Kinetic energy (K.E.) is given by:
K.E. = (1/2) m v²
Momentum (p) is given by:
p = m v
We know:
K.E. = p² / (2m)
Step 2: Express the relationship between K.E. and p
Rearranging:
p² = 2m K.E.
Step 3: Analyze the change in K.E.
If kinetic energy increases by 300%, then the new K.E. is:
New K.E. = Initial K.E. × (1 + 300/100)
New K.E. = 4 × Initial K.E.
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Step 4: Calculate the change in momentum
From the relationship (p² ∝ K.E.):
If K.E. increases by a factor of 4, then:
New p = √(4 × Initial p²)
New p = 2 × Initial p
Thus, momentum increases by 100%.
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