MODEL PAPER 2 PHYSICS. I PUC Time: 3 hours Max Marks: 70

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Buddy Cooper
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1 MODEL PAPE PHYSICS I PUC Time: hour Ma Mark: 7 General Inrucion: i) All par are compulory. ii) Anwer wihou relean diagram / figure/ circui whereer neceary will no carry any mark. iii) Direc anwer o he numerical problem wihou deailed oluion will no carry any mark. PAT A I Anwer he following: X. The SI prefi for -5 i fermi. The epreion for cenripeal acceleraion in erm of angular elociy i a ω c r. kwh i equal o.6 6 J 4. Graiaional conan i defined a he force of aracion which ei beween wo uni mae eparaed by a uni diance. 5. The alue of abolue zero of emperaure i K or -7.5 C 6. Perfec black body i defined a he body which aborb all he radiaion inciden on i. 7. SI uni of pecific hea of a ubance i J kg - K - 8. The equaion for frequency of a fundamenal mode in open pipe i gien by f L Here, m L.m f 85 Hz. 9. λ 4m The diance beween a node and an aninode i gien by 4 λ Bu λ 4m 4 m 4. The paricle aain a minimum acceleraion a he mean poiion. PAT B II Anwer any FIE of he following: 5 X. Conider he equaion m mgh According o he principle of homogeneiy of dimenion, each erm of he phyical quaniy mu be of equal dimenion. LHS HS [ m] [ M ] [ m] [ M ] [ ] [ LT ] [ L T ] [ m ] [ MLT ] [ ML T ] [ ML T ] [ g] [ LT ] [ h] [ L] [ ] [ ] mgh ML T The gien equaion i found o be dimenionally correc.

2 .. (i) (ii). The acceleraion acing on a body eecuing circular moion i known a cenripeal acceleraion. (r ω) ac ac rω r r 4. A rigid body i aid o be under mechanical equnium when i ha no ranlaional and roaional moion. A rigid body i aid o be a no ranlaional moion when i linear elociy i zero or angular acceleraion i. Thi happen only when ecor um of all force acing on a body i zero. F A body i aid o be a no roaional moion only wen ecor um of all he orque acing on he body i zero. i.e., τ 5. i) Thermal radiaion do no require a maerial medium for propagaion and can rael in acuum alo ii) Thermal radiaion alway rael in raigh line. 6. Co-efficien of performance of a refrigeraor i defined a he raio of hea remoed from a low emperaure region o he work done in order o remoe hea. Q Mahemaically, β W Bu W Q Q Q β Q Q β Q Q Q β Q Q Q Q Q T β Bu Q Q T Q β T T β T T T T β T T 7. (i) The frequencie greaer han he fundamenal frequency are called oerone. (ii) The frequencie which are inegral muliple of fundamenal frequencie are known a harmonic. 8. I) elociy i maimum a mean poiion ii) I i minimum a ereme poiion.

3 PAT C III Anwer any FIE of he following: 5 X 5 9. Conider a paricle moing along a raigh line wih uniform elociy. Le be he diance coered by he paricle in a ime wih a elociy. elociy Then, graph of a paricle moing wih uniform elociy i a hown. Area below he cure AB area of recangle OABC A B OC OA ime O C (diplacemen). Conider an objec of ma m moing wih a elociy ''. Then, he linear momenum of he objec i p m le F be he force applied on he objec if dp i he mall change in momenum during a cerain ime d hen, ime rae of change of momenum dp d hen, according o he aemen of Newon nd law of moion, dp F d dp F k where k conan of proporionaliy d Bu p m d(m) F k d d F km d Bu d a d F k ma The alue of k depend upon he yem of uni in SI yem of uni. For he ake of impliciy k F ma. Time of fligh i defined a he ime aken by he projecile o reach a poin of he ame eleaion along i parabolic pah If a and d repreen ime of acen and ime of decen hen, a d f a + d f + f :...() Conider + a bu a - g in θ y in θ + ( g) inθ g g inθ inθ g Subiuing in he equaion () inθ g f

4 . Conider a body projeced from he earh urface wih a elociy equal o ecape elociy ( e) Then he body will neer reurn back o earh and eaily ecape from he graiaional field of he earh A infiniy, EK EP Applying law of coneraion of energy ( E + E ) ( E + E ) K P earh K P inf iniy GMm me + + GMm me m e GMm e GM GM e Bu g g e e e GM g g Thi i he epreion for ecape elociy of he body from he urface of he earh. Elaic colliion Inelaic colliion i) colliion in which linear momenum i) colliion in which linear momenum i and kineic energy are conered conered and i alway a lo of kineic energy. ii) elaic colliion rarely occur in ii) majoriy of he colliion are inelaic naure. colliion. E: colliion beween wo ub-aomic E: A mud ball ruck o he wall paricle. 4. Angular momenum of a paricle i defined a he momen of linear momenum of he paricle and i meaured a he cro produc of poiion ecor [ r ] and liner momenum of he paricle [ p] Conider a paricle of ma m roaing in a circular pah. Le [ r ] be he radiu ecor of he paricle. Then, angular momenum of he paricle i gien by L r p On differeniaion, dl d ( r p ) d d dl dr dp p + r d d d Bu, dr d Alo, dp F d dl p r F d + Bu, p m &

5 r F τ orque dl m +τ d dl ( ) m +τ d dl +τ d dl τ d 5. Sefan 4 h power law ae ha The oal radiaion E from a perfecly black body per econd per uni area i direcly proporional o he fourh power of i abolue emperaure. Mahemaically, E 4 T A E σt 4 A E σt 4 A where σ conan of proporionaliy called Sefan conan and i alue i Wm - K 4 6. The apparen change in frequency of ound due o he relaie moion beween ource of ound and he liener i called Doppler effec i) The ource and liener approach each oher + L f f ii) The liener moe away from he aionary ource f L f PAT D I Anwer any TWO of he following: X 5 7. elociy D B A E o o C ime Conider a paricle moing wih uniform acceleraion along a raigh line. Then he graph of he paricle moing wih uniform acceleraion i hown aboe, where OC ime OA iniial elociy OD final elociy The area below he - cure repreen diance raelled Mahemaically, Diance raelled area blow he cure AB area of rapezium OABC (um of parallel ide) ( diance) (OA + BC)(OC)

6 8. + Bu, + a [ ][ ] [ + + a] [ + a] + a + a + a y-ai P(, y) y y θ -ai Conider a projecile projeced upward wih projecile elociy. Le θ be he angle of projecion. Le P(, y) be he poin reached by he projecile afer a cerain ime along he rajecory. On reoling projecile elociy, horizonal componen o and erical componen y are obained a hown in he diagram. Le and y be he diance coered by he projecile wih repec o poin P. The diance coered along -ai i elociy diance coered ime aken o o coθ Similarly, diance alone y ai i y yo + ( g) y yo g y ( in θ) g co θ co θ g y ( an θ) co θ g y ( anθ ) + co θ Thi equaion reemble he general equaion of a parabola y a + b where a anθ g b co θ Thi clearly how ha, rajecory of a projecile i a parabola.

7 9. Law of coneraion of energy ae ha energy can neiher be creaed nor be deroyed bu can only be ranformed from one form ino anoher form uch ha he ne energy of an iolaed yem alway remain unalered. Conider a body of ma m a a cerain heigh h from he ground. The body i hen allowed o fall freely under he influence of earh graiy. The oal energy E of he body i he um of i kineic energy [E k ] and poenial energy [E p ] E E k + E p A poiion A, E k m E k Bu mgh Ep E E + E k E + mgh E mgh A poiion B, p E mg( h ) p Conider,...() + a Bu,, a + g g Conider, Ek m Ek m( g) Ek mg h (h-) m m m Poiion A E k E p ma Poiion B E k, E p Poiion C E p E E k + E p mg + mg (h - ) mg + mgh mg E mgh...() A poiion C, Heigh h E p Conider, + a Bu, a g, h + gh gh Ek m m gh E E + E p k ( ) E + mgh E mgh...() Comparing eqn. (), () and () i i ery clear ha a freely falling body i in accordance wih law of coneraion of energy.

8 Anwer any TWO of he following: X 5. Conider an objec of ma m placed on he urface of he earh. Le be he cener of he earh, M be he ma of he earh. Applying Newon unieral law of graiaion GMm F g' m The force eered by he earh on he objec ielf i h regarded a he weigh of he objec. F W mg Equaing he aboe equaion, g m GMm mg GM g () M Le he objec be now placed a a heigh of h from he earh urface. Le g be he acceleraion due o graiy a heigh h Applying Newon Unieral law of graiaion. GMm F ( + h) Bu, F W mg Equaing he aboe eqn. GMm GM mg g () ( + h) ( + h) Eqn.() : Eqn. () gie GM g ( + h) g GM g g ( + h) g g h + g g h + g h g + Uing binomial epanion and neglecing higher order erm, we wrie, h h + g h g h g g From he eqn. i i clear ha, acceleraion due o graing decreae wih he increae in heigh.

9 . Conider n mole of an ideal ga filled in a cylinder. Le he ga be allowed epand ery lowly a conan emperaure a decribed in he P- diagram. Toal work done during iohermal proce o epand he ga from A o B i W dw Bu dw Pd W Pd Bu P nt P nt W nt d W nt d d log e [ log ] e W nt W nt loge loge W nt log e W. nt log P P Preure A (P ) W Conider P nt, If T i conan, P conan P Hence, P P P W (.) nt log P P. Newon formula for peed of ound i gien by P ρ According o Newon, peed of ound i gien by where E i modulu of elaiciy E ρ i he deniy of air. ρ For gaeou medium, E k k bulk modulu k () ρ B (P ) olume

10 According o Laplace, he change in preure and olume occur under adiabaic condiion inead of iohermal condiion. The eqn. of ae for an adiabaic proce i P γ conan cp Where γ c Conider P γ conan Taking log on boh ide, log ( P γ e ) conan log P + log γ conan e e On differeniaion, dp + γ d P dp d + γ P dp γ d P The e ign indicae ha wih he increae in preure olume decreae. dp γ d P dp γ P d Bu dp k d K γ P Subiuing K in eqn. (), we ge γ P ρ Thi mahemaical relaion i called Newon Laplace formula for peed of ound. I Anwer any THEE of he following: X 5 5. M kg M? M? 6kmph m/ 5m/.5 m/ By law of coneraion of energy m m + m ( )() m m 5 (5) (.5) m + m 65m m () By applying coneraion of momenum, m u m + m ()() m (5) + m (.5)

11 4. 5m +.5 m () On oling () and () ( 5m +.5 m ) 5 65m m 5 65m +.5m ( ) 65m m 5 m 56.5 m 9.6kg ( ) ( ) m 5m +.5m 5m +.5(9.6) 5m + M.8 kg The mae of he fragmen i.8kg and 9.6 kg. i 8rpm 8 π ω 6π rad 6 f rpm π ω 4π rad 6 min α? θ? n? ω f ωi ω f ωi + α α 6π 4π π.4.5rad θ ω + i α (4 π )() + (.5)() 57 + (.5)(44) rad θ θ π n n π n.4 n roaion for S roaion? 5 5 roaion in

12 5. h 6 km.6 6 m 64 km m M 6 4 kg g 9.8m - i) orbial elociy g + h (6.4 ) ( ) m.69km 6. T K T K η.8 T η T η η. η.7 i) T New emp of he ource T η T.8 T 6 ii) Period of reoluion T π T π T π ( + h) g (( ) ) 6 9.8(6.4 ) T (.4).5 T 6.8( ) T.5 T.94 T T T. T. 5 T T 5K Increae in emp of ource T T 5 5 K ii) T New emp of he ink T η T

13 T.8 7. T.8 T (.) T K Decreae in he emperaure of he ink T T K m ɺ ɺ o f f...() () () f f 6 F 5 f f f m γɺ ɺ F f...() +

TP B.2 Rolling resistance, spin resistance, and "ball turn"

TP B.2 Rolling resistance, spin resistance, and ball turn echnical proof TP B. olling reiance, pin reiance, and "ball urn" upporing: The Illuraed Principle of Pool and Billiard hp://billiard.coloae.edu by Daid G. Alciaore, PhD, PE ("Dr. Dae") echnical proof originally