Question

An object of mass m And Velocity v has kinetic energy 200 J. Find the new kinetic energy if the mass of the object becomes double and velocity still remains the same.

Answer 1

Solution:

$\text{Initial Kinetic Energy} = \dfrac{1}{2} mv^2 = 200 \:J\\\\\\\text{Kinetic Energy after changing is given as:}\\\\\\\rightarrow \dfrac{1}{2}(2m)v^2 \rightarrow mv^2$

The value of mv² can be found out by using the formula of Initial Kinetic Energy. Hence we get:

→ mv² = 200 × 2

→ mv² = 400 J

Hence the new Kinetic energy after the mass is doubled is equal to 400 J.

Alternative Method:

Relation between Kinetic Energy and Mass is given as:

$\boxed{ \text{Kinetic Energy of an object}\:\:\:\:\alpha\:\:\:\:\text{Mass of the object}}$

Hence if mass is doubled, kinetic energy will also be doubled if velocity is constant in both the cases. Hence the final kinetic energy is 400 J.

Answer 2

Answer:

Let the k.e. in first case be x

x = 1/2*m*v^2=200j

in second case

let the kinetic energy be x'

v'=v

m'=2m

x'= 1/2*2m*v^2

x'= 2(1/2*m*v^2)

x'=2(x)

x'=2*200j

x'=400j