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When the mass of a system is variable, a thrust force has to be applied on it in addition to all other forces acting on it. This thrust force is given by stack F with rightwards arrow on top equals stack v with rightwards arrow on top subscript r end subscript open parentheses plus-or-minus fraction numerator d m over denominator d t end fraction close parentheses Here stack v with rightwards arrow on top subscript r end subscriptis the relative velocity with which the mass dm either enters or leaves the system. A car has total mass 50 kg. Gases are ejected from this backwards with relative velocity 20 m/s. The rate of ejection of gas is 2 kg/total mass of gas is 20 kg. Coefficient of friction between the car and road is mu = 0.1 Maximum speed of car will be v = ..... m/s text (Take  end text l text  n  end text fraction numerator 4 over denominator 3 end fraction equals 0.28 text  ) end text

  1. 0.6    
  2. 0.8    
  3. 1.0    
  4. 1.2    

The correct answer is: 0.6

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When two bodies collide normally, they exert equal and opposite impulses on each other. Impulse = change in linear momentum. Coefficient of restitution between two bodies is given by :– e equals fraction numerator text  IRelative velocity of separation  end text I over denominator text  IRelative velocity of approachl  end text end fraction equals 1 for elastic collision Two bodies collide as shown in figure. During collision they exert impulse of magnitude J on each other. If the collision is elastic, the value of J is N–s :

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The tangent at the point P(x1, y1) to the parabola y2 = 4ax meets the parabola y2 = 4a(x + b) at Q and R, the coordinates of the mid-point of QR are

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