Two solids A and B of mass $1 k g$ and $2 k g$ respectively are moving with equal linear momentum. The ratio of their kinetic energies $\frac{K E_{A}}{K E_{B}}$ will be $\frac{A}{1}$ . So the value of $A$ will be ________.

Open in App

Solution

Step 1: Given
Mass of solid A: $m_{A} = 1 k g$
Mass of solid B: $m_{A} = 2 k g$
Linear momentum: $p_{A} = p_{B} = p$
Ratio of kinetic energies of A to B: $\frac{K E_{A}}{K E_{B}} = \frac{A}{1}$
Step 2: Formula Used
$K E = \frac{p^{2}}{2 m}$
Step 3: Find the value of A
Calculate the ratio of kinetic energies of A and B by using the formula
$\begin{array}{rcl} \frac{K E_{A}}{K E_{B}} & = & \frac{\frac{{p_{A}}^{2}}{2 m_{A}}}{\frac{{p_{B}}^{2}}{2 m_{B}}} \\ = & \frac{\frac{p^{2}}{2 \times 1}}{\frac{p^{2}}{2 \times 2}} \\ = & \frac{4}{2} \\ = & \frac{2}{1} \end{array}$
Hence,Two solids A and B of mass $1 k g$ and $2 k g$ respectively are moving with equal linear momentum. The ratio of their kinetic energies $\frac{K E_{A}}{K E_{B}}$ will be $\frac{A}{1}$ . So the value of $A$ will be 2

Suggest Corrections

Similar questions

Q. Two bodies A and B of masses

1

and

4

kg respectively have equal linear momentum. The ratio of their kinetic energies is?

Q. A 4 kg mass and 1 kg mass are moving with equal linear momenta. The ratio of their kinetic energies is

Q. Two masses 1 kg and 4 kg are moving with equal kinetic energies. The ratio of magnitudes of their linear momentum is

Q. Two bodies of masses

m

and

4 m

are moving with equal kinetic energy. Then the ratio of their linear momentum will be

Two particles having masses $4 g$ and $16 g$ respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is $n : 2$ . The value of $n$ will be_____.

Join BYJU'S Learning Program

Two solids A and B of mass 1kg and 2kg respectively are moving with equal linear momentum. The ratio of their kinetic energies KEAKEB will be A1. So the value of A will be ________.

Two solids A and B of mass $1 k g$ and $2 k g$ respectively are moving with equal linear momentum. The ratio of their kinetic energies $\frac{K E_{A}}{K E_{B}}$ will be $\frac{A}{1}$ . So the value of $A$ will be ________.