Misalai 9 na Tambayoyin Faɗaɗawa
1. Takardar ƙarfe a zafin jiki na 20 oC tana da girman da aka nuna a cikin hoton. Idan ma'aunin faɗaɗa ƙarfe mai layi shine 10 -5 o C -1, to ƙaruwar yankin a zafin jiki na 60 oC shine...
A. 0,08 cm2
B. 0,16 cm 2
C. 0,24 cm 2
D. 0,36 cm 2
E. 0,64 cm 2
Tattaunawa
An sani cewa :
Tsawon ƙarfe = 40 cm
Faɗin ƙarfe = 20 cm
Yankin ƙarfe na farko (A o ) = (40)(20) = 800 cm 2
Ma'aunin faɗaɗa layi (α) na ƙarfe = 10 -5 o C -1
Ma'aunin faɗaɗa yanki (β) = ma'aunin faɗaɗa tsawon x 2 (2α) = 2 x 10 -5 o C -1
Bambancin zafin jiki (ΔT) = 60 o C – 20 o C = 40 o C
Tambaya : Ƙara yawan yankin ƙarfe a zafin jiki na 60 oC
Amsa :
Tsarin faɗaɗa yanki :
ΔA = βA o ΔT
Bayanin dabara:
ΔA = ƙaruwa a yanki, β = ma'aunin faɗaɗa yanki, A o = yankin farko, ΔT = canjin zafin jiki = zafin ƙarshe - zafin farko
Ƙara yawan yankin ƙarfe :
ΔA = βA o ΔT
ΔA = (2 x 10 -5 ) (800) (40) = 0,64 cm
Amsar da ta dace ita ce E.
2. Farantin ƙarfe a zafin jiki na 20 oC yana da girma kamar yadda aka nuna a cikin hoton. Idan an ƙara zafin zuwa 100 oC kuma ma'aunin faɗaɗa ƙarfen layi shine 1,1 x 10 -7 o C -1 , to yankinsa yanzu zai zama...
A. 4,0000106 m2
B. 4,0000140 m 2
C. 4,0000376 m 2
D. 4,0000704 m 2
E. 4,0000726 m 2
Tattaunawa
An sani cewa :
Tsawon ƙarfe = mita 2
Faɗin ƙarfe = mita 2
Yankin farko na ƙarfe (A o ) = (2)(2) = 4 m 2
Ma'aunin faɗaɗa layi (α) na ƙarfe = 1,1 x 10 -7 o C -1
Ma'aunin faɗaɗa yanki (β) = ma'aunin faɗaɗa tsawon x 2 (2α) = 2,2 x 10 -7 o C -1
Bambancin zafin jiki (ΔT) = 100 o C – 20 o C = 80 o C
Tambaya : Yankin ƙarfe a zafin jiki na 100 oC
Amsa :
Ƙara yawan yankin ƙarfe :
ΔA = βA o ΔT
ΔA = (2,2 x 10 -7 )(4)(80) = 704 x 10 -7 = 0,0000704 m2
Yankin ƙarfe :
Yankin ƙarfe = yanki na farko + ƙaruwa a yanki
Yankin ƙarfe = 4 m 2 + 0,0000704 m 2
Fadin ƙarfe = 4,0000704 m2
Amsar da ta dace ita ce D.
3. Farantin da aka yi da tagulla (α = 18.10 -6 o C -1 ) a zafin jiki na 0 oC yana da girma kamar yadda aka nuna a hoton. Idan an dumama farantin zuwa 80 o C, to ƙaruwar yankin farantin shine...
A. 0,576.10-4 m2
B. 1,152.10 -4 m 2
C. 2,304.10 -4 m 2
D. 3,456.10 -4 m 2
E. 4,608.10 -4 m 2
Tattaunawa
An sani cewa :
Tsawon tagulla = 40 cm = mita 0,4
Faɗin tagulla = 20 cm = mita 0,2
Yankin farko na tagulla (A o ) = (0,4)(0,2) = 0,08 m 2
Ma'aunin faɗaɗa layi (α) na tagulla = 18 x 10 -6 o C -1
Ma'aunin faɗaɗa yanki (β) = ma'aunin faɗaɗa tsawon x 2 (2α) = 36 x 10 -6 o C -1
Bambancin zafin jiki (ΔT) = 80 o C – 0 o C = 80 o C
Tambaya : Ƙara yawan yankin tagulla a zafin jiki na 80 oC
Amsa :
Ƙara yawan yankin tagulla :
ΔA = βA o ΔT
ΔA = (36 x 10 -6 ) (0,08)(80) = 230,4 x 10 -6 = 2,304 x 10 -4 m2
Amsar da ta dace ita ce C.
4. Jirgin aluminum mai tsawon santimita 20003, cike da ruwa a zafin farko na 0oC. Sannan a yi zafi a cikin tukunya har sai zafin ya kai digiri 90.oC. Idan ma'aunin faɗaɗa layin aluminum shine 24 x 10-6 (oC)-1 kuma yawan faɗaɗar ruwa shine 6,3 x 10-4 (oC)-1, yawan ruwan da ya zubar ya kasance….
A. 100,94 cm 3
B. 100,84 cm 3
C. 100,64 cm 3
D. 100,54 cm 3
E. 100,44 cm 3
Tattaunawa
An san cewa:
Girman farko na bututun aluminum da ruwa (Vo ) = 2000 cm 3 = 2 x 10 3 cm 3
Zafin farko na bututun aluminum da ruwa (T 1 ) = 0 oC
Zafin ƙarshe na jirgin ruwa na aluminum da ruwa (T2 ) = 90 oC
Ma'aunin faɗaɗa layin aluminum (α) = 24 x 10 -6 ( oC ) -1
Ma'aunin faɗaɗa girma na aluminum (γ) = 3α = 3 (24 x 10 -6 ( oC ) -1 ) = 72 x 10 -6 o C -1
Ma'aunin faɗaɗa yawan ruwa (γ) = 6,3 x 10 -4 ( o C ) -1
Tambaya: Yawan ruwan da aka zubar
Amsa:
Tsarin faɗaɗa girma:
V = Vo + γ Vo o ΔT
V – V o = γ V o ΔT
ΔV = γ V o ΔT
Bayani:
V = ƙarar ƙarshe, V o = ƙarar farko, ΔV = canjin girma, γ = ma'aunin faɗaɗa girma, ΔT = canjin zafin jiki.
Lissafa canjin girma na jirgin ruwan aluminum:
ΔV = γ V o ΔT = (72 x 10 -6 )(2 x 10 3 )(90) = 12960 x 10 -3 = 12,960 cm 3
Lissafa canjin da aka samu a yawan ruwa:
ΔV = γ V o ΔT = (6 .3 x 10 -4 )(2 x 10 3 )(90) = 1134 x 10 -1 = 113,4 cm 3
Sauyin da ake samu a yawan ruwa ya fi na aluminum girma, don haka wasu daga cikin ruwan da ke zuba ya yi yawa.
Lissafa yawan ruwan da aka zubar:
113,4 cm 3 – 12,960 cm 3 = 100,44 cm 3
Amsar da ta dace ita ce E.
5. Ana dumama sandar ƙarfe zuwa zafin jiki na 80 oC kuma tsawonsa ya zama 115 cm. Idan ma'aunin faɗaɗa layin ƙarfen shine 3.10 -3 oC -1 kuma zafin farko na ƙarfen shine 30 oC , to tsawon farko na ƙarfen shine….
A. 100 cm
B. 101,5 cm
C. 102 cm
D. 102,5 cm
E. 103 cm
Tattaunawa
An san cewa:
Zafin farko (T)1) = 30oC
Zafin ƙarshe (T)2) = 80oC
Canjin zafin jiki (ΔT) = 80oC - 30oC=50oC
Ma'aunin faɗaɗa layin ƙarfe (α) = 3.10-3 oC-1
Tsawon ƙarfe na ƙarshe (L) = 115 cm
Ana buƙata: Tsawon farko na ƙarfe (L)o)
Amsa:
Tsarin faɗaɗa tsawon:
L = Lo + ΔL
L = Lo + α Lo ΔT
L = Lo (1 + α ΔT)
115 = Lo (1 + (3.10)-3.50) )
115 = Lo (1 + (150.10)-3))
115 = Lo (1 + 0,15)
115 = Lo (1,15)
Lo = 115/1,15
Lo = 100 cm ba
Amsar da ta dace ita ce A.
6. Sanda tagulla da farko tana da tsawon santimita 40. Idan aka dumama ta a zafin jiki na digiri 80 o C, tsawonta zai zama santimita 40,04. Idan ma'aunin faɗaɗa tagulla mai layi shine 2,0 x 10 -5 o C -1 to zafin farko na sandar tagulla shine….
A. 20 oC
B. 22 oC
C. 25 oC
D. 30 oC
E. 50 oC
Tattaunawa
An san cewa:
Zafin ƙarshe (T)2) = 80oC
Tsawon farko (L)o= 40 cm
Tsawon ƙarshe (L) = 40,04 cm
Ƙara tsayi (ΔL) = 40,04 cm – 40 cm = 0,04 cm
Ma'aunin faɗaɗa tagulla (α) = 2,0 x 10-5 oC-1
An tambaya: Zafin farko (T)1)
Amsa:
Tsarin faɗaɗa ƙarfe:
L = Lo + α Lo ΔT
L - Lo = α Lo ΔT
ΔL = α Lo ΔT
ΔL = α Lo (T2 - T1)
0,04 = (2,0 x 10-5)(40)(80 – T1)
0,04 = (80 x 10-5)(80 – T1)
0,04 = 0,0008 (80 – T)1)
0,04 = 0,064 – 0,0008 T1
0,0008 T1 = 0,064-0,040
0,0008 T1 = 0,024
T1 = 30oC
Amsar da ta dace ita ce D.
7. Takardar ƙarfe a zafin jiki na 20oC yana da girma kamar yadda aka nuna a hoton. Idan ma'aunin faɗaɗa layin ƙarfe shine 10-5 oC-1 sannan karuwar yankin a zafin jiki na 60oC shine…
A. 0,08 cm2
B. 0,16 cm2
C. 0,24 cm2
D. 0,36 cm2
E. 0,64 cm2
Tattaunawa
Wannan tambayar tana da alaƙa da faɗaɗawa.
An sani :
Tsawon ƙarfe = 40 cm
Faɗin ƙarfe = 20 cm
Yankin ƙarfe na farko (A)o) = (40)(20) = 800 cm2
Ma'aunin faɗaɗa layi (α) na ƙarfe = 10-5 oC-1
Ma'aunin faɗaɗa yanki (β) = ma'aunin faɗaɗa tsawon x 2 (2α) = 2 x 10-5 oC-1
Bambancin zafin jiki (ΔT) = 60oC - 20oC=40oC
An tambaya : Ƙara yawan yankin ƙarfe a zafin jiki na 60oC
Jawab :
Tsarin faɗaɗa yanki :
ΔA = βAo ΔT
Bayanin dabara:
ΔA = ƙaruwa a yanki, β = ma'aunin faɗaɗa yanki, Ao = yankin farko, ΔT = canjin zafin jiki = zafin ƙarshe - zafin farko
Ƙara yawan yankin ƙarfe :
ΔA = βAo ΔT
ΔA = (2 x 10-5)(800)(40) = 0,64 cm
Amsar da ta dace ita ce E.
8. Farantin ƙarfe a zafin jiki na 20oC yana da girma kamar yadda aka nuna a hoton. Idan zafin jikian ɗaga shi zuwa 100oC kuma ma'aunin faɗaɗa ƙarfe mai layi shine 1,1 x 10-7 oC-1, to yankin yanzu ya zama…
A. 4,0000106 m2
B. 4,0000140 m2
C. mita 4,00003762
D. 4,0000704 m2
E. 4,0000726 m2
Tattaunawa
An sani :
Tsawon ƙarfe = mita 2
Faɗin ƙarfe = mita 2
Yankin farko na baƙin ƙarfe (A)o) = (2)(2) = 4 m2
Ma'aunin faɗaɗa layi (α) na ƙarfe = 1,1 x 10-7 oC-1
Ma'aunin faɗaɗa yanki (β) = ma'aunin faɗaɗa tsawon x 2 (2α) = 2,2 x 10-7 oC-1
Bambancin zafin jiki (ΔT) = 100oC - 20oC=80oC
An tambaya : Yankin ƙarfe a zafin jiki na 100oC
Jawab :
Ƙara yawan yankin ƙarfe :
ΔA = βAo ΔT
ΔA = (2,2 x 10-7)(4)(80) = 704 x 10-7 = 0,0000704 m2
Yankin ƙarfe :
Yankin ƙarfe = yanki na farko + ƙaruwa a yanki
Yankin ƙarfe = 4 m2 + 0,0000704m2
Yankin ƙarfe = 4,0000704 m2
Amsar da ta dace ita ce D.
9. An yi faranti da tagulla (α = 18.10-6 oC-1) a zafin jiki na 0oC yana da girman kamar yadda aka nuna a hoton. Idan an dumama farantin zuwa 80 oC, to, ƙaruwar yankin farantin shine...
A. 0,576.10-4 m2
B. 1,152.10-4 m2
C. 2,304.10-4 m2
D. 3,456.10-4 m2
E. 4,608.10-4 m2
Tattaunawa
An sani :
Tsawon tagulla = 40 cm = mita 0,4
Faɗin tagulla = 20 cm = mita 0,2
Yankin tagulla na farko (A)o) = (0,4)(0,2) = 0,08 m2
Ma'aunin faɗaɗa layi (α) na tagulla = 18 x 10-6 oC-1
Ma'aunin faɗaɗa yanki (β) = ma'aunin faɗaɗa tsawon x 2 (2α) = 36 x 10-6 oC-1
Bambancin zafin jiki (ΔT) = 80oC - 0oC=80oC
An tambaya : Ƙara yawan yankin tagulla a zafin jiki na 80oC
Jawab :
Ƙara yawan yankin tagulla :
ΔA = βAo ΔT
ΔA = (36 x 10-6)(0,08)(80) = 230,4 x 10-6 = 2,304 x10-4 m2
Amsar da ta dace ita ce C.
Tushen tambaya:
Tambayoyin Nazarin Fizik na Ƙasa ga Makarantar Sakandare ta Babbar Sakandare/Makarantar Sakandare ta Sana'a
