Question

Three boys are standing on a horizontal paltform of mass $170\text{kg}$ and length $6\text{m}$ is as shown in figure. They exchange their position as shown in the figure. Distance moved by the platform is : (Neglect friction)

• A. $0.35\text{m}$
• B. $0.55\text{m}$
• C. $0.45\text{m}$
• D. $0.25\text{m}$

Answer 1

The correct option is A $0.35\text{m}$

Initially, centre of mass of system wrt left edge of platform is,
$x_i=\frac{(60\times 1)+(40\times 3)+(80\times 5)\times (170\times 3)}{60+40+80+170}$
$x_i=\frac{1090}{350}=\frac{109}{35}\text{m}$
After persons exchange their positions,
$x_f=\frac{(80\times 1)+(60\times 3)+(40\times 5)+(170\times 3)}{80+60+40+170}$
$x_f=\frac{970}{350}=\frac{97}{35}\text{m}$
Since, no external force is present, the position of centre of mass remains fixed and platform is moved by,
$x_i-x_f=\frac{109-97}{35}\approx 0.35\text{m}$