Physics-
General
Easy

Question

A mass ‘m’ moves with a velocity 'v’ and collides in elastically with another identical mass. After collision the Ist mass moves with velocity fraction numerator v over denominator square root of 3 end fraction in a direction perpendicular to the initial direction of motion. Find the speed of the 2nd mass after collision

  1. fraction numerator 2 over denominator square root of 3 end fraction v    
  2. fraction numerator v over denominator square root of 3 end fraction    
  3. v    
  4. square root of 3 blank v    

The correct answer is: fraction numerator 2 over denominator square root of 3 end fraction v


    Let mass A moves with velocity v and collides inelastically with mass B comma which is at rest

    According to problem mass A moves in a perpendicular direction and let the mass B moves at angle theta with the horizontal with velocity v
    Initial horizontal momentum of system
    (before collision) equals m v ….(i)
    Final horizontal momentum of system
    (after collision) equals m V cos invisible function application theta ….(ii)
    From the conservation of horizontal linear momentum
    m v equals m V cos invisible function application theta rightwards double arrow v equals V cos invisible function application theta …(iii)
    Initial vertical momentum of system (before collision) is zero
    Final vertical momentum of system fraction numerator m v over denominator square root of 3 end fraction minus m V sin invisible function application theta
    From the conservation of vertical linear momentum
    fraction numerator m v over denominator square root of 3 end fraction minus m V sin invisible function application theta equals 0 rightwards double arrow fraction numerator v over denominator square root of 3 end fraction equals V sin invisible function application theta …(iv)
    By solving (iii) and (iv)
    v to the power of 2 end exponent plus fraction numerator v to the power of 2 end exponent over denominator 3 end fraction equals V to the power of 2 end exponent left parenthesis sin to the power of 2 end exponent invisible function application theta plus cos to the power of 2 end exponent invisible function application theta right parenthesis
    rightwards double arrow fraction numerator 4 v to the power of 2 end exponent over denominator 3 end fraction equals V to the power of 2 end exponent rightwards double arrow V equals fraction numerator 2 over denominator square root of 3 end fraction v

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