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Question
Four bodies A,B,C and D of masses [MA=m, MB=2m, MC=m, MD=2m] are initially at rest. They start moving under the influence of the internal force of attraction and at a particular instant, their velocities are −→VA=2^i, −→VB=−^i+2^j and −→VC=−2^i+2^j. Find the velocity of body D (−→VD) at that instant.
Four bodies A,B,C and D of masses [MA=m, MB=2m, MC=m, MD=2m] are initially at rest. They start moving under the influence of the internal force of attraction and at a particular instant, their velocities are −→VA=2^i, −→VB=−^i+2^j and −→VC=−2^i+2^j. Find the velocity of body D (−→VD) at that instant.
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Solution
The correct option is B ^i−3^j
Bodies are moving under effect of mutual force therefore no net external force on the system.
⇒ No net acceleration of the system.⇒acom=0
Velocity of COM before bodies start moving is zero therefore velocity of COM will remain zero even after they start moving.
→Vcom=mA−→VA+mB−→VB+mC−→VC+mD−→VDmA+mB+mC+MD
0=m(2^i)+2m(−^i+2^j)+m(−2^i+2^j)+2m−→VDm+2m+m+2m
⇒2^i+2(−^i+2^j)+(−2^i+2^j)+2−→VD=0
⇒2−→VD=2^i−6^j
⇒−→VD=^i−3^j
Bodies are moving under effect of mutual force therefore no net external force on the system.
⇒ No net acceleration of the system.⇒acom=0
Velocity of COM before bodies start moving is zero therefore velocity of COM will remain zero even after they start moving.
→Vcom=mA−→VA+mB−→VB+mC−→VC+mD−→VDmA+mB+mC+MD
0=m(2^i)+2m(−^i+2^j)+m(−2^i+2^j)+2m−→VDm+2m+m+2m
⇒2^i+2(−^i+2^j)+(−2^i+2^j)+2−→VD=0
⇒2−→VD=2^i−6^j
⇒−→VD=^i−3^j
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