Question

Two objects of masses $200g$ and $500g$ possess velocities $10\hat{i}$ $m/s$ and $3\hat{i}+5\hat{j}$ $m/s$ respectively. The velocity of their centre of mass in $m/s$ is

• A. $5\hat{i}-25\hat{j}$
• B. $\frac{5}{7}$$\hat{i}-25\hat{j}$
• C. $5\hat{i}+\frac{25}{7}\hat{j}$
• D. $25\hat{i}-\frac{5}{7}\hat{j}$

Answer 1

The correct option is C $5\hat{i}+\frac{25}{7}\hat{j}$

Given,

Mass of A and B

$M_A=0.2kgand{M}_B=0.5kg$

Velocity of A and B

$V_A=10\hat{i}m/sand{V}_B=3\hat{i}+5\hat{j}m/s$

From the conservation of momentum

$M_A{V}_A+M_B{V}_B=M_{total}{V}_{cm}$

$V_{cm}=\frac{M_A{V}_A+M_B{V}_B}{M_{total}}=\frac{0.2\left(10\hat{i}\right)+0.5(3\hat{i}+5\hat{j})}{0.2+0.5}$

$V_{cm}=5\hat{i}+\frac{25}{7}\hat{j}$

Velocity of center of mass $5\hat{i}+\frac{25}{7}\hat{j}$