Question

Two bodies A and B having masses in the ratio of 1:2, have velocities in the ratio 2:3. Ratio of their momenta is
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Answer 1

Anѕwєr :

1:3

Exρlαnαtion :

As per the provided information in the given question, we have :

• Two bodies A and B having masses in the ratio of 1:2.
• And, velocities in the ratio 2:3.

We've been asked to calculate the ratio of their momentum.

Let us assume the masses of A and B as 1x and 2x. And let their velocities be 2y and 3y.

$\Large\underline{\pink{\frak { Momentum :}}}$

• In Physics, Momemtum is defined as the amount of motion contained in the body. It is calculated by finding the product of mass and velocity. In simple words, Momentum is the product of mass and velocity. Its SI unit is kg.m/s.

$\mapsto{\boxed{\red{\sf{ p= mv}}}}$

• p denotes momentum
• m denotes mass
• v denotes velocity

Now, let us assume the ratio of their momentum be R. According to the question,

$\implies\sf{R = \dfrac{Momentum_A}{Momentum_B}}$

$\implies\sf{R = \dfrac{p_A}{p_B}}$

$\implies\sf{R = \dfrac{m_Av_A}{m_Bv_B}}$

$\implies\sf{R = \dfrac{1x.2y\; kg.ms^{-1}}{2x.3y\; kg.ms^{-1}}}$

$\implies\sf{R = \cancel{\dfrac{2xy \; kg.ms^{-1}}{6xy\; kg.ms^{-1}}}}$

$\implies\sf{R = \dfrac{1}{3}}$

$\implies \boxed{\red{\sf{R = 1\ratio 3}}}$

∴ Ratio of their momentum is 1 : 3.

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