Question

Compare the kinetic energies of two objects of masses 10kg and 50kg respectively have same momentum

Answer 1

KE=Psquare/2M

KE is inversly proportional to mass. 2 bodies of same momemtum but different masses then the larger mass has less KE and the smaller mass has more KE.x^{2}x

2

Answer 2

Explanation:

Momentum of a body moving with velocity v and mass m is given by,

P = mass times velocity

P = m v

Given masses 10kg, 50 kg.

For 10 kg mass, Let its velocity be u

Momentum of 10 kg mass = 10u

For 50 kg mass, Let its velocity be v

Momentum of 50 kg mass = 50v

Given Momentum of both masses are equal.

10u = 50v

u : v = 50 : 10

u : v = 5 : 1

Kinetic energy of a body of mass m, moving with velocity v is given by

K = 0.5 mv²

Ratio of kinetic energies will be,

K₁: K₂

$\begin{gathered} = \frac{0.5 \times 10 \times u ^{2} }{0.5 \times 50 \times {v}^{2} } \\ \\ = \frac{1}{5} \times ( \frac{u}{v} ) ^{2} \\ \\ = \frac{1}{5} \times( \frac{5}{1} ) ^{2} \\ \\ = \frac{25}{5} \\ \\ = \frac{5}{1} \\ \\ = 5 \ratio \: 1\end{gathered}$

Therefore, The kinetic energies will be in the ratio 5 :1