BABAK PENYISIHAN SELEKSI TINGKAT PROVINSI
BIDANG BIDANG KOMPETISI
Babak Penyisihan Seleksi Tingkat Provinsi , 27 September 2011 , OSNP ERTAMINA 2011 Soal -soal osnpertamina.com osnpertamina.com di download d i www .osnpertamina.com
1
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Olimpiade Sains Nasional Pertamina 2011 Petunjuk :
1. Tuliskan secara lengkap isian pada Lembar Jawab Komputer 2. Ujian seleksi ini terdiri dari 50 soal pilihan g anda eti ap nomor jika dijawab di jawab benar akan diberi nilai 4 poin; poin ; namun jika dijawab 3. Setiap poin . salah akan diberikan nilai -1 poin. 4. Disediakan waktu 120 menit 5. Gunakan pensil 2B untuk menjawab 6. Semua jawaban harus ditulis di lembar jawaban yang tersedia 7. Peserta dapat mulai bekerja bila bila sudah ada tanda mulai dari pengaw as. 8. Peserta harus segera berhenti bekerja bila ada tanda berhenti dari Pengawas. 9. Letakkan lembar jawaban di meja sebelah kanan dan segera meninggalkan ruangan. 10. Tidak diperkenankan menggunakan kalkulator kalkulator.
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Pilihlah Pilihlah jawaban yang paling tepat
1. Interak Int eraksi si antara atom-atom dalam molekul diatomik di atomik yang yang memili memiliki ki ikatan lemah dapat dijelaskan melalui potensial Lennard -Jones, yaitu:
Molekul Mol ekul terse ter sebut but bervibr ber vibras asii dari posisi posisi seimbang. seimbang. Tent entukan ukan frekuens fr ekuensii angular angular vibras vibr asii molekul jika massa masing-masing atom adalah m dan jarak antar atom dalam kadaan seimbang ad alah ro. A. B. C.
D. E.
2. Sebuah sistem zat padat magnetik terdiri dari N atom persatuan volume ditempatkan dalam medan magnet homogen B. Tentukan magnetisasi sistem tersebut pada
temperatur temperatur T jika setiap atom atom memiliki spin ½ d an momen magnet µ. A. B. C.
D. E.
3. Bahan germanium memiliki celah energi antara pita valensi dan pita konduksi sebesar 0,67 eV. Untuk mengeksitasi elektron dari pita valensi ke pita konduksi secara optik dibut uhkan gelombang gelombang elektromagne elekt romagnett ik dengan dengan panjang gelombang gelombang maksimum maksimum sekit sekit ar
... . A. B. C
414 nm 618 nm 1019 nm
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4. Sebuah bahan bahan semikonduktor semikondukt or silikon (Si) di-dope dengan arsenik (As). Anggap satu dari lima elektron elektr on valens valensi arsenik arsenik beredar beredar membentuk membentuk orbit Bohr di sekitar t iap-tiap ion As+ dalam kisi silikon t ersebut ersebut.. Jika Jika masa masa efektif efekt if elektron elekt ron dalam bahan bahan terse t ersebut but sebesar ebesar 0,31 kali kali masa masa elektron elektr on bebas dan dan konstanta dielektrik dielektr ik silikon ili kon sebes sebesar ar 12, maka maka jarijari jari - jari
orbit Bohr pertama elektron tersebu t adalah ... . A . 20,5 Å B . 1,97 Å C . 0,53 Å D . 0,21 Å E . 0,014 Å sel surya (solar cell) cell ) dapat dimodelkan sebaga sebagaii suat suat u devais yang t erdiri erdir i atas 5. Sebuah sel sebuah sumber arus ideal (sumber arus listrik yang dihasilkan dari hasil konversi intensitas cahaya), I ph ; sebuah dioda ideal, I d ; sebuah hambatan shunt, Rsh
dan
sebuah hambatan seri, R s yang digambarkan sebagai berikut.
R s I ph
I d
R sh
Dioda merupakan suatu devais yang bersifat non -ohmic no n - o hmic , yang memiliki karakteristik
I V sebagai I
Io e
V
1 , dengan
dan I o adalah konstanta. Dengan
dan R s 0 , ada dua karaktr karaktr tisti k solar solar cell yang dapat dapat dicari yaitu menganggap Rsh V oc : tegangan solar cell pada saat open circuit dan I sc : arus solar cell pada saat close circuit . Pernyataan yang benar adalah: A . I sc = 0 B . I sc = I o C . I sc = I p h
D . V oc E.
V oc
1
1
ln
ln
Io e
I ph I o I sc I o
V
1
1
1
6. Sebuah bola pejal berjari-jari r dan bermassa m mulai menggelinding tanpa slip di atas permukaan dalam sebuah silender berlubang dengan jari-jari dalam R (Lihat gambar di
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B. C.
D. E.
7. Gaya gravitasi bekerja pada sebuah benda titik bermassa m yang diakibatkan oleh sebuah sebuah benda bermassa bermassa M berbent ber bentuk uk seperempat seperempat lingka li ngkaran ran berjari-j berj ari-jari ari R, R, sepert sepert i
terlihat pada gambar di bawah ini. Tentukan besar gaya gravitasi tersebut. A. B.
M
C.
D. E.
m
R
8. Sebuah partikel bergerak pada lingkaran berjari- jari R yang terletak di bidang datar. Vektor posisi partikel terhadap titik P berotasi dengan kecepatan sudut tetap (lihat gambar). Bagaimanakah persamaan gerak partikel tersebut terhadap titik Q? A. B.
0 0 C. 0 D. 0 0 E.
2
sin
2 2 2
sin cos
2
R Q
P
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9. Sebuah sistem terdiri dari katrol A, katrol B, dan tiga balok. Massa katrol diabaikan, sedangkan massa balok adalah M1
M2
M 3 (lihat gamb ambar). ar). Katrol Katrol A terg t ergantung antung di
t empat empat yang t etap, et ap, sedang sedangkan kan kat kat rol B tergantung pada ka katt rol A. Jika dianggap dianggap tidak ti dak ada gesekan pada sistem , berapakah percepatan M 1 ? A. B. C.
D. E.
M1
2M 2
2M 3
M1
2M 2
2M 3
g
A
M1M 2
M1 M 3
4 M 2 M 3
M1M 2
M1 M 3
4 M 2 M 3
M1M 2
2M 2 M 3
M1 M 3
M1M 2
2M 2 M 3
M1 M 3
4 M1
M2
M 3
4 M 1
M2
M 3
M1M 2 2
M2
g
M 1
B
g
M1 M 3
M1
g
2
M 2 M 3 M 3
2
g
M 2 M 3
batang ang identik, ident ik, masing-mas masing-masing ing panjangnya panjangnya L , dihubungkan dengan engsel E pada 10. Dua bat satu ujungnya, kemudian diletakkan diletakkan di atas lantai dengan sudu t 0 terhadap horisontal (lihat gambar). Jika percepatan gravitasi g dan geseka gesekan n diabaikan, berapa lama l ama waktu
yang dibutuhkan hingga eng sel turun menyentuh lantai? A.
B.
C.
D.
E.
3 L 2g 3 L 2g 2 L 3g 2 L 3g 2 L 3g
0
0 0
0 0
0 0
0 0
0
d
1 2 sin d
1 2s 2 sin d
1 2 sin d
1 sin d
1 sin
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E
0
st asiun asiun ruang angkas angkasa a selalu selalu t eramat eramat i di atas tempa t empatt yang sama sama di permukaa per mukaan n 11. Sebuah st bumi. Jika jari-jari bumi R , periode rotasi bumi T , dan percepatan gravitasi di gorbit? permukaan bumi g , pada ketinggian berapa dari pusat bumi stasiun itu men gorbit? A.
B.
C.
D.
E.
2 2 2 R T g
1/ 3
2
R 2T 2 g
2
2
2
2
R T g
1/ 3
1/ 3
2
2
2
4
2
R T g
2 2 4 R T g
1/ 3
1/ 3
2
12. Sebuah bandul sederhana (massa m digantung dengan tali tak bermassa yang panjangnya l ) berada di ruang bebas gravit gravitas asii (misalnya pesawa pesawatt ruang angkas angkasa). a). Agar Agar bandul itu beada dalam medan gravitasi dilakukan dengan cara titik pivot diputar dengan dengan kecepatan kecepatan sudut t erhadap erhadap sat sat u t it ik poros, yang berjarak berj arak R dari R dari titik pivot bandul, pada bidang yang da datt ar yang sama sama sepert sepertii dit unjukkan pada p ada gamba gambar. r. Sehingga ehingga bandul itu mengalami gerak osilasi seolah berada dalam medan gravitasi g
2
R.
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1
A. L
2 1
B . L
2 1
C . L
D . L E. L
2 1 2 1 2
m x2
y2
m
2
R
m
2
R2
m
2
m
2
2
m l
2
Rl (1 cos ) 2
2
2
l2
2 Rl
cos
2 Rl
cos
m
2
Rl (1 cos )
R2
R2
m
2
Rl (1 cos )
bo la pejal digantung pada ttali ali yang ringa ri ngan, n, masing-mas masing-masing ing mass massanya adalah adalah 13. Tiga buah bola m, M dan 4m . 4m . Ketiga bola itu hampir saling bersentuhan, Bola bermassa 4m dirent dir entang angkan kan sehingga sehingga ketinggiannya ket inggiannya h. Massa M agar M agar diperoleh ketinggian maksimum adalah
:
l h
A. M B . M
2m 0.5m
C . M
4m
D . M
0.25m
E. M
m
14. Sebuah bola pejal bermassa m bergerak rolling tanpa slip pada suatu silinder yang berotas berot asii dengan dengan kecepatan kecepatan sudut sudut gesek F f
. Sehingga ehingga antara bola dan silinder silin der terdapa ter dapatt gaya
esek st st atik antara sili silinde nderr dan bola adala adalah h N (koefisien gesek
). Bola Bola itu
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0 , karena bola mengalami
A . Bola mungkin bergerak dengan kecepatan sudut N percepatan centripetal
upaya ya bola tidak t idak berputar berput ar di t empat empat , maka maka pada bola it u harus ada tors tor si sebe ebes sar B . Supa ô
d L s
a F f dt C . Arah kecepatan kecepatan sudut bola,
dan silinder, silinder ,
momentum sud ut bola yang bergerak spin, D . Arah kecepatan kecepatan sudut bola,
adalah searah dengan rˆ
Ls
dan silinder, silinder ,
momentum sud ut bola yang bergerak spin, E.
berlawanan, karena arah dari
relasi antara kecepatan sudu t bola,
searah, karena arah dari
adalah searah dengan rˆ
Ls
dan silinder,
adalah
2 5
jar i r berada 15. Lubang berbent berbentuk uk lingkaran l ingkaran dengan dengan jarijari - jari r berada di dasar dasar t empat empat penampunga penampungan n air (toren). (t oren). Diketahui iket ahui kerapat kerapat an air ada adalah lah
. Mula-mula Mul a-mula t empat empat penampunga penampungan n itu it u
ditutupi dengan bola bermassa m , jari - jari jar i R dengan R > r . Karena ada kebocoran, maka ketingg keti nggian ian air semakin semakin lama l ama sema semakin kin berkurang berkur ang.. Pada saa saatt mencapa mencapaii ketinggian ket inggian tertentu h o , penyumbat lubang it u t erangkat. erangkat. Deng engan an mengang mengangga gap p seluruh bagian bagian o , bola penyumbat bola masih masih t ercelup ercelup air, ma maka ka ketinggian ketinggian h o o itu adalah: (hint: volume bola terpancung
adalah: V ( r , R )
3
2R
3
2R
2
r
2
R
2
2
r
)
ho R
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16. Sebuah sistem tabung gas berisi gas diatomik dan monatomik dalam fraksi tertentu. Deraj Derajat at disos disosiasi iasi didef didefin inisikan isikan sebaga sebagaii
di mana
adalah massa massa gas
monat monat omik dan dan m adalah massa total sistem. Massa atomik gas monatomik adalah A
g/mol. Persamaan keadaan gas tersebut adalah ... . A. B. C.
D. E.
17. Dalam suatu sistem termodinamika, satu mol gas ideal mengalami proses sehingga entropi gas tersebut berubah terhadap temperatur T dapat dinyatakan sebagai , di mana a ada adalah lah konst konst ant ant a posit positifif,, dan dan C v adalah kalor jenis molar pada volume volume konstan. konst an. Tent Tentukan ukan t emperatur gas gas pada pada proses t ersebut ersebut sebagai ebagai fungs f ungsii volume jika pada T = T 0 0 , V = V 0 . A. B. C.
D. E.
18. Persamaan keadaan gas Van der Waals dinyatakan sebagai berikut: , di mana a dan b adalah kons tanta. Koefisien ekspansi volume, untuk gas gas Van der Waals adalah ... .
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19. Andaikan persamaan fundamental dari sebuah sistem termodinamika dapat dituliskan sebagai u
R
R
s2
v
2 0
u energi dalam per mol, s entropi s entropi per mol, v 2 , dengan u energi
dan v volume v volume per mol, serta R ,? ? dan v 02 adalah konstanta-konstanta. Suhu (T (T ) dari sistem tersebut dapat diekspresikan sebagai A. B. C.
R R v02
2
D.
E.
2 2
s
R
R v02
R 2 v02
v
v
Andaikan t ersedia ersedia sejuml sejumlah ah zat zat cair cair dengan dengan kapasit kapasit as panas panas C v bersuhu T 1 yang 20. Andaikan ditempatkan dalam lingkungan udara yang bersuhu T 0, di mana T 1>T 0 (T 0 dan T 1 dalam Kelvin). Karena T 1>T 0 air akan melepaskan panas ke reservoir udara. Secara prinsip, sebag sebagian ian panas yang dilepas dil epaskan kan air ini i ni dapat dapat dimanfaatkan dimanfaat kan untuk unt uk diubah menjadi menj adi kerja. kerj a. Jika kit a dapat dapat mengatur mengatur agar agar proses t ransfer panas dari air ke udara terjadi ter jadi seca secara ra ehingga ent entropi ropi t otal ot al air dan dan udara tidak t idak berubah, berubah, maka kerja maksimum maksimum reversible , sehingga
yang dapat dihasilkan dapat dihitung sebagai … . T 1
A.
W
1
C v
T 1
T
T 0 T 1
B.
W
1
C v T 0 T 1
C
W
C
1
T 0
T T 1
T
dT
dT
dT
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C.
D. E.
T 0 2 T 0 4 T 0
22. Entropi dari sebuah paramagnet ideal dalam medan magnetik diberikan secara pendekatan oleh S S 0 aU 2 , di mana U energi sistem spin dan S 0 dan a adalah konstanta-konstanta. Dari persamaan di atas hubungan antara U dan T dapat diturunkan sebagai … . A . U B . U C.
U
D . U E.
U
1 2aT 1 aT 1 aT 1
2aT a T 2
23. Dua mol gas helium berada pada tekanan 1 atm dan temperatur 273 K. Tekanannya lalu dit di t urunkan seca secara ra adiabatik adiabati k sampai sampai 0,4 atm. Diketahui iket ahui kapasit kapasitas as panas panas gas gas helium Cp = 5,004 kal.K-1.mol-1 dan Cv = 3,014 kal.K-1.mol-1. Temperatur akhir gas helium adalah
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25. Satu setengah k ilogram air (H2O) dipanaskan sehingga berubah seluruhnya menjadi uap pada 100 100 °C dan teka t ekanan nan tet t etap ap 1 atm. Diketahui iket ahui kalor penguapa penguapan n air 540 kal.g-1. Massa Massa jenis jenis uap uap air pada pada tem t empe pera ratt ur 100 100 °C da dan tekana tekanan n tetap 1 atm yaitu yaitu 0,59 0,593 3 kg/ kg/ m3.
Perubahan energi dalam H 2O adalah …. A . 4,2 MJ B . 3,2 MJ C.
2,2 MJ
D . 1,2 MJ E.
0,2 MJ
listrik gelombang elektrommagnet elektrommagnet yang merambat pada sumbu z 26. Komponen medan listrik diyatakan sebagai berikut:
Komponen medan magnet gelombang EM tersebut adalah ... . A. B
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28. Seorang mahasiswa mahasiswa Fisika Fisika mencoba menggulung menggulung kawat konduktor kondukt or yang memiliki memili ki panjang d dan jari-jari r ke suatu induktor berbentuk silinder dengan penampang lingkaran lingkaran berjari-jari berjari-j ari R. R. Kawat Kawat digulung sec secara ara ket ket at t anpa anpa terjadi t erjadi t umpang umpang tindih t indih antar
kawat. Induktansi Induk tansi diri induktor tersebut adalah ... . A. B. C.
D. E.
29. Komponen medan listrik dan medan magnet gelombang elektromagnet dinyatakan sebagai berikut: dan RataRata -rata Intensitas gelombang EM tersebut terhadap waktu adalah ... . A. B. C.
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31. Sebuah magnet A yang sangat sangat pendek bermass b ermassa a m digantungkan dengan seutas tali panjangnya l . Ada m agnet agnet lain B yang juga sangat sangat pen dek d idekatkan secara perlahan perlahan lahan ke magnet A, sedemikian rupa sehingga sumbu horizontal selalu sama. Pada saat magnet A berjarak s dari posisi awal dan jarak antar magnet adalah d , magnet A secara secara spont spont an bergerak dan menem pel ke m agnet agnet B. Diketahui Diketahui int eraksi eraksi gaya magnet adalah Fmagnet ( x)
K x
n
. Tentukan nilai n
l
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A.
bahan itu berupa bola kosentrik
B . RC C . RC
D . R E.
C
4 1 4 1 d A A
(dengan A : luas penampang, d: jarak jara k efek e fektif tif anta a ntarr titik titi k A dan da n B) B)
d
33. Seutas kabel koaksial, diameter bagian dalam r 1 dan diameter bagian luar r 2 , diantaranya diant aranya diisolas dii solasi.i. Salah Salah satu satu ujung uj ung kabel itu it u dihubungkan denga dengan n batere V dan ujung lainnya dihubungkan hambatan R seperti ditunjukkan pada gambar berikut. Karena arena diberi bat bat ere, maka diant diant ara kabel kabel koaksial koaksial itu it u t imbul medan medan listri l istrik. k. Seba ebaliknya liknya
karena pada ujung lainnya diberi hambatan, maka akan ada arus yang mengalir di kabel
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S
V
o
2 rR
E.
34. Osilasi medan listrik dinyatakan sebagai E
Eo sin kz
t yang merambat dalam
udara (hampa secara elektromagnet), dengan k : bilang bil angan an gelombang, gelombang, : frekuens fr ekuensii sudut, E o : amplitudo medan listrik, dan z : osilas osilasii gelombang dalam arah sumbu-z. sumbu-z. Jik Jika a
osilasi ini merupakan osilasi gelombang elektromagnet, maka memenuhi: A. B.
1 k
B
o
o
Bo sin kz E 2
t , dengan
B : induksi
medan magnet
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A.
1
k
2
m k
B. C.
m
3
k
2
m
D. 2 E.
k m
5
k
2
m
37. Jika A sebuah operator kuantum dan A† adalah conjugate hermitiannya, maka di antara pilihan pilihan berikut, kombinasi operat operator yang tidak memiliki sifat hermitian
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0
V
dengan V bil V bilang angan an kompleks kompl eks.. 0 Jika dihit dihi t ung dengan dengan teori t eori perturbasi pert urbasi sampai sampai pendekat pendekat an orde ke-2, harga-harga harga-harga energi perturbasinya dapat dituliskan sebagai H '
sistem tsb setelah dikoreksi adalah ... . A.
A
B.
A
C.
A
D. E.
| V | 2 A B 2 | V | A B A B
| V |
2
A B
1
2
2 1
A B
dan
B
dan
B
dan
B
| V | 2 A B 2 | V | A B A B
| V |
2
A B
2
4 AB | V | 2
A B
2
4 AB | V | 2
V *
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D.
2
(4
) x
(
2
2
2
2
H
m 2
E.
) x
42. Diketahui
2
1
m
dan
sama. Jika
1
H
2
*
adalah keadaan eigen ternormalisasi yang memiliki nilai eigen 2
d
a
bagaimanakah kombinasi linier A. B.
1
2
2 2a a 2 1 2 2a
dengan d 1
dan
2
elemen volume dan a bilangan ril,
yang ortonormal terhadap
1
+
2
?
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A.
0
B.
2a0
C.
5a02
D.
6a0
E.
10 a0
2
2
2
45. Tingkatan energi untuk partikel bermassa m yang terperangkap dalam ruang 1 dimensi 0 x a adalah 2
E n
2
n 2
2
.
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atom Z diberikan oleh rumus 47. Energi ikat nuklir dengan nomor massa A dan n omor atom semi-empiris E
a1 A a 2 A
2/3
a3
Z ( Z 1) 1/ 3
A
a4
( A 2Z ) 2 A
n
a5 A
3/ 4
dengan n ( 1,0) . Suku manakah y ang merupakan koreksi energi asimetri?
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50. Nukleon memiliki memili ki spin ½ dan isospin isospin ½. ½. Jika Jika sebuah sebuah inti int i berada ber ada pada pada keadaa keadaan n dasar, dasar, volumenya V , nilai momentum Fermi (momentum tertinggi ) nukleon penyusunnya pF , maka inti tersebut tersusun dari A nukleon, dengan nilai A menurut model inti gas Fermi adalah ….