igcse cambridge physics as solving p 2 feb 2026

Forces rate of change of momentum. SI unit will be kilogram m/ second minus one. This is for momentum as momentum is mv and rate of means division by time which is by second. So it is kilogram mus 2. So for left hand side it is m/ second minus one for right hand side it is force in SI units it is kilogram mus 2 is in over kilogram for mass and for area meter / 2 can make elimination to have right hand side meters again -3. So as those sides are not the same, we cannot say that it is homogeneous. Total momentum before equal total momentum after. Certainly if no external force applied. We will apply conservation of momentum in horizontal direction. And before collision only the sack was moving horizontally with this speed. Its mass is 23 kilogram. After collision we have both boat and sack move as one object. So after collision we have 160 + 23. Okay. And it is the velocity after that is required. So we can make this product equal to 23 * 3.4 four from which we can get read as. Okay. is half which is 160 + 23 that is 83. Okay. Time v². This is the velocity that we have just calculated. It was 3 all squared. This is half mv² over a1 also half. And the only mass that has velocity before was mass of sack which is 23 and was 3.4 per second all squared. We can certainly remove half with have and use calculator to find the answer as boy 13 certainly inelastic and this is because E2 is less than E1 and this is shown here from ratio of E2 by E1 less than one means E2 less than E1. Okay, for the boat to be at rest, we should have weight equal to the uprust applied by motor on the boat. So abs is equal to certainly it's not only the boat, it is the boat with this hack. Okay. So, is 183 times acceleration due to gravity. It will give some numbers that can be rounded to 1,800 Nton. We know also equal row density of liquid volume of liquid displaced. So it equals by rearrangement. This is was just calculated here converted by multiplying by 10 to minus 6. Okay. 1,00 kilogram cube minus one mus 3. This is typical value for density of water. So we have here work against resistive force and we know that work equal FD distance along the track on which there is resistive force. So = divided by and is 23. Okay, it is clear that we will use the formula for delta GB. So we should note here that change in kinetic energy from to to is converted to increase in GB. Okay. and in work done against the resistive force or canon to overcome this resistive force. Okay. So as Ka at point should equal work done against resistor force plus increase in GB plus the remaining kinetic energy at We want the we want the GB to be subject. So it's kinetic energy at minus work against friction minus netic energy at all divided by mg. This gives delta directly. can then substitute. I'll make all the kilojles as it is. Just multiply here by 10 to three. Here is mass. Okay. It will be less because although there is an increase in kinetic energy comes from the returning back to same level. So increase in delta GB will go back to to kinetic energies too. But from to we still have fraction. So we will not have the very similar value of 13 one as remember. sorry 16.1 we will not come here to or the same value of KJ for kinetic energy but it will be little less than this value. So, Ka at is less than this at which means at less than at and this is because there is friction from to Okay. moment is force times perpendicular distance from boy to belt. Moment of weight about is zero because line of action of weight is passing by or perpendicular distance is equal to zero. To calculate theta, it is obvious that we have component of vertical component of here which is sin theta and have same on the other side and both vertical components should balance with weight because we are in equilibrium. So if we add these two up forces and equating them with the weight okay we can find C2 okay and say here 2 * think tension is moving here. Yes. 13 Newton. Okay. And if let the arrangement be in another step here the weight is 19. So we can say directly that theta is sin -1 19 over 2 * 13 which is 26. So is 47°. Okay, we know that you models exist stress over strain and we have the strain. We want the strain and we have both stress and area. We have the diameter. So we have it. So from this equation we can rearrange like that sigma over and sigma is sorry we have here youngest modus but sigma we don't have sigma so we need to dismantling it to force over area * 1 / The force on the wire is the tension. Okay. And value of tension is 13 Newton. So it is 13 over area is this is the diameter radius will be 04 which is 0.004 0 O4 okay meter squared * this is the area time 1 / value given for youngest modest 9.3 * 10 210 10. Your calculator should find the final answer is okay. We have question of motion = + half t² is 0 is neglected and by rearrangement is square root of 2 over So, okay. So from another equation of motion v² we can find the by again neglecting ^ 2 is equal to zero from rest we have square of 2 square of square root of 2 is same as square roo of 2 * square root of So the relation here between and is not linear. It is root function and root function is drawn like this. Okay. We can also calculate the exact value of his at the 1.6. 6 If you plugged this 1.6 in this equation, you can get the value of 5.6 Six period time of one complete oscillation amplitude maximum displacement from equilibrium. Okay, you can say this is antinode. This is antinode. This is antinode. is equal to lambda We have here of 25. We just need lambda. We have from the figure here length of string and how many nodes and anti nodes form on this list see here 1.5 lambda to be equal this length which means It's lamb equals 64 We can substitute here. So = which equals When frequency becomes 30, this mean lambda equals over 16 / 30. choose 16 because it doesn't change this weight. So lambda after the increase in frequency will be this value. And if we divide the length over half of this value, this is the wavelength. Half of wavelength. Okay. If we divide total length over half of wnets we will get 3.6 which is not multiple of lambda / two. And to have stationary waveform, we should have length of string to contain multiples of lambda over two. Okay. Lambda equal sin theta and do we need So it is sin theta divided by lambda. is 1 / denasty which is given in question Okay. Sin theta is sin 37 and 1 / lambda will be 1 / 4.5 * 10 - 3. This all gives this value. Okay. We will round this value to one. We will round it down. So is equal to one. Okay. Having your line deny means the decreases 1 / increases 1 / is the Okay. And we have sin theta from the equation lambda= sin theta. We have sin theta to equal lambda / Okay. As increases sin theta and theta will decrease. As sin theta decreases. We know that sin theta is also equal to / is the distance from the right spot and the is distance from the grating to the screen. So as sin theta or theta decreases should be less and as decreases spacing between fringes also decreases. Okay. rate of charge fluid. Okay. To draw this relation between terminal tension difference and current. We need to remember that this relation is VB minus IIR. Okay. So this is straight line equation with some part cut from the yaxis and this part is VB. VB here is 1.5. So we will use the rule starting by 1.5 and we should end somewhere here. If we looked carefully, we will find that internal resistance which is 0.5 7 is this low. Okay, we can certainly write IR as Here is here is So this is the slope. And we can make this slope here. Clearly if this was to 1.8 2. If it was like that, we would have to just make this line to the two because we have 1.5 as vertical difference divided by two as horizontal difference. This certainly gives us the slope of 0.75. But the graph just ended at 1.6. So we cannot draw this line to for example cannot draw it like this. We should draw it up. But where is exactly up? It is simple to find if we substituted 1.6 in this equation. So we have which is equal to 1.5 - 0.75 Okay. If we substitute by 1.6 six we will have the value of 0.3 volt. So we should stop somewhere here at.3 volt. If all of this is 0.5 so very small square is 0.05 05 and to reach three we reach 3 we can simply divide like this we will get six very small squares. So this line should be adjusted just to have six small it. Okay. Okay. So resistivity from R= row / row is equal to / is given is given to is given So, so we have here the answer. okay. meter. And if we want to calculate Okay, we can do this. Calculate the total resistance in the circuit. It will be this times the resistance of the wire. Okay. divided by and in same time total is equal to the terminal retention tension out of the battery which is VB minus current in circuit times internal resistance which is potential drop across the internal resistance. So VB minus this potential drop gives us the potential between the terminals. This potential is applied on So if we divide it by the current we can find Okay. Okay. Sorry. We can only find our total not through because if we want to find if we want to find for terminal potential we should divide by in this branch not in the circuit. circuit is divided to two parts I1 and I2. So if we were to just divide terminal potential by some current value to get this current value should be I1. But we don't have I1. So if we divide terminal potential by total current in circuit, we get total resistance. Okay, just be careful when applying Ohm's law. Know specifically which current with which resistance you apply the low or the formula to. Okay, this gives us our total and we can substitute in this equation and rearrange. We can find something like this. Okay, just made cross product here. Okay, from this you can easily get as this. power dissipated it is squared Okay. And once again be careful for which resistor the question asks about. So it is the internal resistance are small. So current in circuit this is the current that bus is in the internal resistor and this is the value of internal resistance. The answer should be certainly in what? Okay. Structure of nuclear atom is nucleus. Okay. where mass and positive charge are concentrated. Okay. And electrons would say that revolve and orbits. Okay. two elements, one with 94 and one with 91 protons. Okay, both decay form 92 protons with respect to This is decrease by two. So it is alpha with respect to This is an increase by one. So it is beta negative where neutron is neutral decay to proton and beta negative and electron anti neutrino. So we know that charge is 1.6. This is the elementary charge. And if we divided it by mass of proton, we will not get this number. If we divide it by mass of proton sorry, mass of electron, okay, we will get this. No, but here is positive sign. So this is positive. So particle is positive. Beta positive particle. Thank you for watching. Keep following us.