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  • A man of mass 80 Kg stands on a plank of mass 40 Kg. The plank is lying on a smooth horizontal floor. Initially, both are at rest. The man starts walking on the plank towards the north and stops af

A man of mass 80 Kg stands on a plank of mass 40 Kg. The plank is lying on a smooth horizontal floor. Initially, both are at rest. The man starts walking on the plank towards the north and stops after moving a distance of 6m on the plank. The plank will move 

Option: 1

6m , south 


Option: 2

4m , north 


Option: 3

4m , south 


Option: 4

6m , north 


Answers (1)

best_answer

As we have learned

If External Force = 0 -

\vec{P}_{total} = constant

- wherein

i.e. if no external force is acting on the system, net momentum of the system remains constant.

 

 As 

F_{ext} = 0 \\\\ so \: \: \vec a_{cm}= 0 \: \: \: \vec v_{cm}= cost =0 \\\\ \vec v_{cm}=\frac{m_1\vec v_1+m_2\vec v_2}{m_1+m_2}=0 \\\\ or \: \: m_1v_1+m_2v_2= 0 \\m_1\frac{dx_1}{dt}+m_2\frac{dx_2}{dt}=0\\\\or\: \: m_1\vec x_1+ m_2 \vec x_2 = 0

x_1 = (6-x) \\x_2 = -x \\\\ m_1 (6-x) - m_2x = 0 \\\\\8 0(6-x ) = 40 x\\\\x = 4m , south 

Posted by

Rakesh

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