Momentum is defined as the product of an object's mass and velocity. It is a vector quantity and its unit is kg m/s. The momentum of an object is conserved in the absence of any external force acting on the object.

Kinetic energy is defined as the energy possessed by an object due to its motion. It is a scalar quantity and its unit is Joule (J). The kinetic energy of an object is directly proportional to the square of its velocity and the mass of the object.



The relation between momentum and kinetic energy can be derived using the formula for kinetic energy and momentum.

Kinetic energy (K) = 1/2 x m x v^2

Momentum (p) = m x v

where m is the mass of the object and v is the velocity of the object.

Substituting the value of v from momentum equation in the kinetic energy equation, we get:

K = p^2 / 2m

From the above equation, we can see that the kinetic energy of an object is directly proportional to the square of its momentum and inversely proportional to its mass.



Let us assume that the initial momentum of the object is p1 and the final momentum after the 10% increase is p2.

The percentage increase in momentum can be calculated as:

% increase in momentum = (p2 - p1) / p1 x 100

= (0.1 x p1) / p1 x 100

= 10%

Therefore, the momentum of the object increases by 10%.



Using the above relation between momentum and kinetic energy, we can calculate the percentage increase in kinetic energy as:

% increase in kinetic energy = [(p2^2 / 2m) - (p1^2 / 2m)] / (p1^2 / 2m) x 100

= [(1.1p1)^2 / 2m - p1^2 / 2m] / (p1^2 / 2m) x 100

= (1.21 - 1) x 100

= 21%

Therefore, the kinetic energy of the object increases by 21% when the momentum is increased by 10%.



In conclusion, the kinetic energy of an object is directly proportional to the square of its momentum. When the momentum of an object is increased by 10%, its kinetic energy increases by 21%. This relationship is important in understanding the motion of objects and the transfer of energy between them.