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# If the K.E of the body is quadrupled then momentum of the body doubles.(a) True(b) False

Last updated date: 26th Feb 2024
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Hint: Kinetic energy is the energy that an object absorbs to change its location, and it is dependent on mass and velocity. Momentum is equal to the product of the square of speed and half of the mass, while kinetic energy is equal to the product of the square of speed and half of the mass.

An object's kinetic energy is the energy associated with it as it moves. It's described as "the amount of energy needed for a body to accelerate from rest to a specified velocity." It's a quantity with a vector.
$K.E = \dfrac{1}{2}m{v^2}$
Where,
m=mass of the object measured in kg
v= velocity of the object measured in m/s
Momentum: The virtue of an object's mass is its momentum. It's referred to as the mass-velocity product. It's a quantity with a vector attached to it.
$p = mv$
Where
P= momentum.
M= mass of the object measured using kg.
V= velocity of object measure using m/s.
Here we can see that Momentum is directly proportional to the velocity as given in the equation for momentum
So, based on the knowledge gathered so far, we can deduce that kinetic energy is directly proportional to velocity squared. This means that when momentum is doubled while mass remains constant, velocity is also doubled, resulting in a fourfold increase in kinetic energy over the original value. So, the above given statement is true.
Hence, the correct option is (a).

Note: Important properties related to kinetic theory
Energy is neither gained or lost when molecules collide.
The molecules in a gas take up very minute space in relation to the container they occupy.
The molecules are in constant, linear motion.