# If the momentum of an object is increased by 10% then its kinetic energy will increase by?

By Ritesh|Updated : November 8th, 2022

If the momentum of an object is increased by 10% then its kinetic energy will increase by 21%. Steps to calculate the increase in kinetic energy:

Step 1. Using the momentum definition

The relationship between velocity and mass is known as momentum.

Step 2. Using the Kinetic energy definition

The quantity of energy that a particle or object has as a result of its motion is known as kinetic energy.

Step 3. It is given that

Final momentum = initial momentum + (10%) of initial momentum.

Step 4. We can calculate

Kinetic energy (KE)1 = p2/2m ….. (1)

Where p is the momentum, m is the mass of the body,

If we increase p by 10%,

Final p = p + p/10 = 11p/10, Substitute value of p in (1), we get

(KE)2 = (11p/10)2/2m = 121/100 . p2/2m = 121/100 . (KE)1

Change in kinetic energy, Δ KE = (KE)2 - (KE)1

= 121/100 (KE)1 - (KE)1

= (KE)1 [121/100 - 1]

= 21/100 (KE)1

So Δ KE/ (KE)1 x 100 = 21

The term used to describe the state of motion of an object with a mass greater than zero is momentum. As a result, momentum can be applied to any moving object.

Thus, if momentum increases by 10%, kinetic energy will change by 21%.

Summary:

## If the momentum of an object is increased by 10% then its kinetic energy will increase by?

An object's kinetic energy will rise by 21% if its momentum increases by 10%. Momentum is the property of the connection between mass and velocity. GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com