Question

the momentum of an object is doubled how does its kinetic energy change

Answer 1

Dear student,
let mess m, and velocity v
kinetic energy =( 1/2)mv²
And momentum = mv
kinetic energy(E) related by momentum(p) by
E = p²/(2m)
Now if momentum is doubled,
Initial momentum is p₁=p and finally p₂= 2p
So, E₁= p²/(2m)
and finally
E₂= (2p)²/(2m) = (4p²)/(2m) = 4E₁
So if momentum doubled kinetic energy change by 4 times.
Regards