Q.Two objects A and B of masses 2 kg and 10 kg respectively are moving with same velocity. The ratio of their momentum will be :

Momentum p = mass x velocity, so its SI unit is kg m s^-1 (equivalently, N s).

Linear momentum of a body is defined as:

p = m v

where m is mass (unit: kg) and v is velocity (unit: m/s = m s^-1).

Multiplying the units: kg x (m s^-1) = kg m s^-1.

This can be checked against the options:

(a) Kg m s^-1 -- matches the definition exactly. …

Since momentum $p=mv$ and both objects share the same velocity, the momentum ratio reduces to the mass ratio, 1:2.

Given: $m_A = 5\text{ kg}$, $m_B = 10\text{ kg}$, both moving with the same velocity $v$.

Formula: Momentum $p = mv$.

…

With the same velocity, momentum is directly proportional to mass, so the ratio of momenta equals the ratio of masses.

Momentum: $p = mv$.

Given $m_A = 2\ \text{kg}$, $m_B = 10\ \text{kg}$, and both moving with the same velocity $v$: …

Momentum $p = mv$; at equal velocity, the particle with the greatest mass has the greatest momentum — that is the $\alpha$-particle.

Step 1 — Recall the momentum formula.

For a particle of mass $m$ moving with velocity $v$,

$p = mv$

Since all four particles here move with the same velocity $v$, momentum is directly proportional to mass: the heavier particle has the larger momentum.

Step 2 — Compare the masses.

• $\beta$-particle = a fast electron, mass $\approx 9.11\times10^{-31}\text{ kg} \approx 1/1836\,u$
• proton, mass $\approx 1.67\times10^{-27}\text{ kg} \approx 1u$
• neutron, mass $\approx 1.675\times10^{-27}\text{ kg} \approx 1u$ (marginally heavier than the proton) …

Since p = mv and v is the same for all four particles, the one with the largest mass has the largest momentum — the α-particle.

Linear momentum is $p = mv$. All four particles here move with the same velocity v, so p ∝ m: whichever particle is heaviest carries the greatest momentum.

Approximate rest masses:

• β-particle (an electron): $m_e \approx 9.1\times10^{-31}$ kg
• Proton: $m_p \approx 1.673\times10^{-27}$ kg
• Neutron: $m_n \approx 1.675\times10^{-27}$ kg (slightly more than the proton) …