A cart of mass M is tied to one end of a massless rope of length 10 m . The other end of the rope is in the hands of a man of mass M, the entire system is on a smooth horizontal surface. The man is at x=0 and the cart at x=10 m . If the man pulls the cart by a rope, the man and the cart will meet at the point

Question

A cart of mass M is tied to one end of a massless rope of length 10 m . The other end of the rope is in the hands of a man of mass M, the entire system is on a smooth horizontal surface. The man is at x=0 and the cart at x=10 m . If the man pulls the cart by a rope, the man and the cart will meet at the point (A) x = 0 (B) x=5m (C) x=10m (D) They will never meet

Tardigrade Admin · Accepted Answer

They meet at the centre of mass xC O M=(m1 x1 + m2 x2/m1 + m2) =(M × 0 + M × 10/2 M)=5m

$x = 0$

$x = 5 m$

$x = 10 m$

They will never meet

They meet at the centre of mass
$x_{COM} = \frac{m _{1} x _{1} + m _{2} x _{2}}{m _{1} + m _{2}}$
$= \frac{M \times 0 + M \times 10}{2 M} = 5 m$

x=0

x=5m

x=10m

They will never meet

They meet at the centre of mass xCOM​=m1​+m2​m1​x1​+m2​x2​​ =2MM×0+M×10​=5m

$x = 0$

$x = 5 m$

$x = 10 m$

They meet at the centre of mass
$x_{COM} = \frac{m _{1} x _{1} + m _{2} x _{2}}{m _{1} + m _{2}}$
$= \frac{M \times 0 + M \times 10}{2 M} = 5 m$