Question

Find the ratio of magnitude of linear momentum, if two bodies A and B of mass 9 Kg and 25 Kg respectively are moving with equal kinetic energy.
1. 2 : 3
2. 5 : 3
3. 3 : 2
4. 3 : 5

Answer 1

Correct Answer - Option 4 : 3 : 5

CONCEPT:

Kinetic Energy:

• The energy possessed by a particle by the virtue of its motion is called kinetic energy. It is given by,

​
\(⇒ KE=\frac{1}{2}m× v^{2}\)    

Linear momentum:

• It is defined as the product of the mass of an object, m, and its velocity, v. It, is a vector quantity.​

⇒ P = mv   

Where KE = kinetic energy, P = linear momentum, m = mass and v = velocity

• The relation between the kinetic energy and the momentum is given as,

⇒ P2 = 2mKE

CALCULATION:

Given that : m_A = 9 Kg, m_B = 25 Kg, and KE_A = KE_Bm
m

• The relation between the kinetic energy and the momentum is given as,

⇒ P2 = 2mKE

• Momentum for body A is

\(\Rightarrow P^2_A=2m_A\times KE^2_A=18\times KE\)      ------ (1)

• Momentum for body B is

\(\Rightarrow P^2_B=2m_B\times KE^2_B=50\times KE\)      ------ (2)

On dividing equation 1 and 2, we get

\(⇒\frac{P_{A}}{P_{B}}=\sqrt{\frac{9}{25}}=\frac{3}{5}\)

⇒ P_A : P_B = 3 : 5

• Hence option (4) is correct.