First slide

Motion of centre of mass

Question

Figure shows a boy on a horizontal platform A on a smooth horizontal surface, holding a rope attached to a box B. Boy pulls the rope with a constant force of 50 N. The combined mass of platform A and boy is 250 kg and that of box B is 500 kg. The velocity of A relative to the box B 5 s after the boy on A begins to pull the rope, will be :

Moderate

A

1 m/s
B

1.5 m/s
C

2 m/s
D

0.5 m/s

Solution

$\large 50 = 250\,{a_A} \Rightarrow {a_A} = 0.2\,m/{s^2}$
$\large -50 = 500\,{a_B} \Rightarrow {a_B} = - 0.1\,m/{s^2}$
$\large {a_{AB}} = 0.3\,m/{s^2}$
$\large {V_{AB}} = {a_{AB}}\,t = 1.5\,m/s$

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