Question

Three bodies $P$, $Q$, and $R$ have masses $m\text{ kg}$, $2m\text{ kg}$, and $3m\text{ kg}$ respectively. If all the bodies have equal kinetic energy, then the greater momentum will be for body/bodies

• A. $Q$
• B. $R$
• C. $P$ and $Q$
• D. $P$

Hint:

A useful conceptual shortcut to remember for physics exams is: under equal kinetic energy constraints, the heavier body always carries more momentum ($p \propto \sqrt{m}$). Conversely, under equal momentum constraints, the lighter body always carries more kinetic energy ($E_k \propto \frac{1}{m}$).

Answer 1

The Correct Option is B

Step 1: Understand the question.
Three bodies $P, Q, R$ have masses $m$, $2m$, $3m$ and the same kinetic energy. We must find which has the greatest momentum.
Step 2: Link momentum and kinetic energy.
Kinetic energy can be written using momentum as \[ E = \frac{p^2}{2m}. \] Rearranging for momentum, \[ p = \sqrt{2mE}. \]
Step 3: Note what is common.
All three bodies have the same kinetic energy $E$. So $p = \sqrt{2mE}$ depends only on the mass: bigger mass means bigger momentum.
Step 4: Compare the masses.
Since $p\propto\sqrt{m}$ and the masses are $m < 2m < 3m$, the momenta follow the same order.
Step 5: Pick the largest.
The largest mass is $3m$, which belongs to body $R$. So $R$ has the greatest momentum.
Step 6: State the answer.
Body $R$ has the greatest momentum. \[ \boxed{R\ \text{has the greatest momentum}} \]