physics
mechanics
Easy

Question

Particles of masses 2 M, m and 3 M are respectively at points A, B and C with AB=1/4(BC). m is much-much smaller than M and at time t=0, they are all at rest. At subsequent times before any collision takes place

  1. m will move towards 2 M.
  2. m will remain at rest.
  3. m will move towards 3 M.
  4. m will have oscillatory motion.

The correct answer is: m will move towards 2 M.


    Force on mass at B due to mass 2M at A is
    F subscript 1 equals fraction numerator G M cross times 2 M over denominator left parenthesis A B right parenthesis squared end fraction along BA
    F subscript 2 equals fraction numerator G m cross times 3 M over denominator left parenthesis B C right parenthesis squared end fraction along BC
    table attributes columnalign left end attributes row cell F subscript R equals F subscript 1 minus F subscript 2 end cell row cell equals fraction numerator 2 G m M over denominator left parenthesis A B right parenthesis squared end fraction minus fraction numerator G m cross times 3 M over denominator left parenthesis B C right parenthesis squared end fraction end cell row cell because A B equals 1 fourth B C end cell end table
    because F subscript R equals fraction numerator 2 G m M over denominator open parentheses 1 fourth B C close parentheses squared end fraction minus fraction numerator 3 G m M over denominator left parenthesis B C right parenthesis squared end fraction  along BA
    equals fraction numerator 29 G m M over denominator left parenthesis B C right parenthesis squared end fraction along BA

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