Question

A man of mass $80 \, kg$ is riding on a small cart of mass $40 \, kg$ which is rolling along a level floor at a speed of $2 \, m \, s^{- 1}$ . He is running on the cart so that his velocity relative to the cart is $3 \, m \, s^{- 1} \, $ in the direction opposite to the motion of the cart. What is the speed of the centre of mass of the system

• A. $1.5ms^{- 1}$
• B. $1ms^{- 1}$
• C. $3ms^{- 1}$
• D. zero

Answer 1

Answer: (D)

$\overset{ \rightarrow }{v}_{c a r t}=\overset{ \rightarrow }{v}_{c}=2\hat{i}$
$\Rightarrow \overset{ \rightarrow }{v}_{m}=\overset{ \rightarrow }{v}_{m c}+\overset{ \rightarrow }{v}_{c}$
$\Rightarrow \left(\overset{ \rightarrow }{v}\right)_{m}=\left(- 3 \hat{i}\right)+2\hat{i}$
$\Rightarrow \overset{ \rightarrow }{v}_{m}=\hat{i}$
Now $\left(\overset{ \rightarrow }{v}\right)_{c m}=\frac{80 \left(- \hat{i}\right) + 40 \left(2 \hat{i}\right)}{80 + 40}$
$\overset{ \rightarrow }{v}_{c m}=0$