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    text  Two particles of equal mass have velocities  end text v with not stretchy rightwards arrow on top subscript 1 equals 4 i with not stretchy hat on top text  and  end text v with not stretchy rightwards arrow on top subscript 2 equals 4 j with not stretchy hat on top m s to the power of negative 1 end exponent text  First particle end text text   has an acceleration  end text a with not stretchy rightwards arrow on top subscript 1 equals left parenthesis 5 i with not stretchy hat on top plus 5 ȷ with not stretchy hat on top right parenthesis m s to the power of negative 2 end exponent text  while the acceleration of the other particle is end text text   zero. The centre of mass of the two particles moves in a path of  end text

    1. circle
    2. parabola
    3. Ellipse
    4. Straight line

    The correct answer is: Straight line

      v with not stretchy rightwards arrow on top subscript 1 equals 4 i with not stretchy hat on top straight m divided by sec semicolon v with not stretchy rightwards arrow on top subscript 2 equals 4 j with not stretchy hat on top straight m divided by sec space of 1em a subscript 1 equals 5 i with not stretchy hat on top plus 5 j with not stretchy hat on top straight m divided by straight s squared semicolon a subscript 2 equals 0 v with not stretchy rightwards arrow on top subscript c m end subscript equals fraction numerator m subscript 1 v with not stretchy rightwards arrow on top subscript 1 plus m subscript 2 v with not stretchy rightwards arrow on top subscript 2 over denominator m subscript 1 plus m subscript 2 end fraction equals fraction numerator m left parenthesis 4 i with not stretchy hat on top plus 4 j with not stretchy hat on top right parenthesis over denominator 2 m end fraction semicolon v with not stretchy rightwards arrow on top subscript c m end subscript equals fraction numerator 4 square root of 2 over denominator 2 end fraction equals 2 square root of 2 straight m divided by sec straight a with not stretchy rightwards arrow on top equals fraction numerator straight m subscript 1 straight a with not stretchy rightwards arrow on top subscript 1 plus straight m subscript 2 straight a with not stretchy rightwards arrow on top subscript 2 over denominator straight m subscript 1 plus straight m subscript 2 end fraction equals fraction numerator straight m left parenthesis 5 straight i with not stretchy hat on top plus 5 straight j with not stretchy hat on top right parenthesis plus straight m left parenthesis 0 right parenthesis over denominator 2 straight m end fraction straight a subscript straight infinity equals 1 half times 5 square root of 2 equals fraction numerator 5 over denominator square root of 2 end fraction straight m divided by straight s squared

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      space Two particles of masses space 100 gm text  and  end text 300 gm space space have at a given time velocities space left parenthesis 10 i with hat on top minus 7 j with hat on top minus 3 k with hat on top right parenthesis text end text text and  end text left parenthesis 7 i with hat on top minus 9 j with hat on top plus 6 k with hat on top right parenthesis cms to the power of negative 1 end exponent text  respectively.  Then velocity of centre of mass  of the system in  end text cms to the power of negative 1 end exponent text is  end text

      space Two particles of masses space 100 gm text  and  end text 300 gm space space have at a given time velocities space left parenthesis 10 i with hat on top minus 7 j with hat on top minus 3 k with hat on top right parenthesis text end text text and  end text left parenthesis 7 i with hat on top minus 9 j with hat on top plus 6 k with hat on top right parenthesis cms to the power of negative 1 end exponent text  respectively.  Then velocity of centre of mass  of the system in  end text cms to the power of negative 1 end exponent text is  end text

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      F i g u r e space s h o w s space a space u n i f o r m space d i s c space o f space r a d i u s space R comma space f r o m space w h i c h space a space h o l e space o f space r a d i u s space R divided by 2 space h a s space b e e n space c u t space o u t space f r o m space l e f t o f space t h e space c e n t r e space a n d space i s space p l a c e d space o n space t h e space r i g h t space o f space t h e space c e n t r e space o f space t h e space d i s c. space F i n d space t h e space C M space o f space t h e space r e s u l t i n g space d i s c.

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