nkhul;Lit gy;fiyf;fof nghwpapaw;gPl jkpo; khztu;fs;

elhj;Jk; fh.ngh.j cau;ju khztu;fSf;fhd

gapw;rpg; guPl;ir - 02

ngsjPftpay;

Gs;sp toq;Fk; jpl;lKk;

gy;Nju;T tpdhf;fSf;fhd tpsf;fTiuAk;

gy;Nju;T tpdhf;fSf;fhd tpilfs;

Q Ans Q Ans Q Ans Q Ans Q Ans

01. 3 02. 2 03. 2 04. 1 05. 3

06. 2 07. 4 08. 5 09. 1 10. 4

Gs;spj;jpl;lk;

gFjp 𝑰 = 𝟏𝟎 × 𝟐 = 𝟐𝟎 Gs;spfs;

gFjp 𝑰𝑰 = 𝟓𝟎 Gs;spfs;

gFjp 𝑰𝑰𝑨(mikg;Gf;fl;Liu tpdh)= 𝟏 × 𝟐𝟎 = 𝟐𝟎 Gs;spfs;

gFjp 𝑰𝑰𝑩(fl;Liu tpdh)= 𝟏 × 𝟑𝟎 = 𝟑𝟎 Gs;spfs;

nkhj;jk; = gFjp 𝑰 +gFjp 𝑰𝑰

= 𝟐𝟎 + 𝟓𝟎 = 𝟕𝟎 Gs;spfs;

= 𝟕𝟎

𝟕𝟎× 𝟏𝟎𝟎 = 𝟏𝟎𝟎 Gs;spfs;

gy;Nju;T tpdhf;fSf;fhd tpilfSf;fhd tpsf;fTiufs;

(1) a – Fw;wpfspd; Mu;KLfy;

F = ma

Fw;wp B , → R = mB × a --------- ①

njhFjp , → F = (mA + mB) × a --------- ②

①, ② ⇒ R = mB

(mA+mB) × F

↑ ↑ ↑

y = m × x

mB

(mA+mB) = tanθ

⇒ mA

mB = cotθ – 1

(2) R J}uj;jpy; <u;g;G Mu;KLfy; = 25

1.5 R J}uj;jpy; <u;g;G Mu;KLfy; = g' vd;f

g = GM

R2 ⇒ gR2 = GM = khwpyp

25 × R2 = g' × (1.5R)2

g' = 11.11 N kg⁄

(3) Tl;l mstpilapd; ,opT vz;zpf;if = 1

2𝑚𝑚

50=

1

100= 0.01 𝑚𝑚

Ntzpau; mstpilapd; ,opT vz;zpf;if = 1

2𝑚𝑚 −

9

10× 0.01 𝑚𝑚 = 0.001 𝑚𝑚

fUtpapd; thrpg;G = 11 x 0.5 mm + 4 x 0.01 mm + 3 x 0.001 mm

= 5.543 mm

(4)

≡

V2 = (14

9⁄

149⁄ + 1

) 5 = 70

23 V

V = V3 = (4

4 + 3)

70

23 = 1.739 V

(5) ntg;g tpisT fhuzkhf ,ioapd; ntg;gepiy mjpfupf;Fk;. MfNt ,ioapYs;s fw;wad;fs; mjpu;tjhy; RahjPd ,yj;jpud;fs; mira ,lk;nfhLf;fhJ. vdNt ntg;gepiy mjpfupf;Fk; NghJ jilj;jpwd; mjpfupf;Fk;.

(6) 1

v -

1

u =

1

f ⇒

1

−2.5 -

1

100 =

1

f ⇒ f = 2.43 cm

(7)

A ,y; PV=nRT ,l 3 × 105 × 2 × 10−3 = 𝑛 × 𝑅 × 300

𝑛 =2

𝑅

B ,y; khwhf;fdtsT vdNt 𝑃 𝛼 𝑇 9×105 𝛼 𝑇2

3×105 𝛼 𝑇1 𝑇1 = 300 𝐾

𝑇2 = 900 𝐾 ⟹ 627℃ ∆𝑈 = 𝑛𝐶𝑣∆𝑇

∆𝑈 =2

𝑅×

3𝑅

2× 600 = 1800 𝐽

(8)

f ' = (1500 + 𝑣 2⁄

1500 − 0 ) 15 × 106

f '' = (1500 + 0

1500 − 𝑣 2⁄ ) f '

f '' = (1500 + 0

1500 − 𝑣 2⁄ ) (

1500 + 𝑣 2⁄

1500 − 0 ) 15 × 106 = (

1500 + 𝑣 2⁄

1500 − 𝑣 2⁄ ) 15 × 106

f '' - 15 × 106 = 8 × 103

(1500 + 𝑣 2⁄

1500 − 𝑣 2⁄ ) 15 × 106 - 15 × 106 = 8 × 103

v = 0.8 m s-1

(9) B apd; kPbwd; < A apd; kPbwd;

mbg;G kPbwd; = 5

2⁄

5150⁄

= 75 Hz

B apd; kPbwd; = 150 Hz - 75 Hz = 75 Hz

(10) VBE = 0 ⇒ VB = 0

𝛽 =𝐼𝑐

𝐼𝑩= 50 100 kΩ ,w;F FWf;Nf V=IR ,l

12𝑉 = 𝐼𝑩 × 100 × 103Ω ⟹ 𝐼𝑩 = 3

25 𝑚𝐴

𝐼𝑐 = 50 ×3

25 𝑚𝐴 = 6 𝑚𝐴

𝑉𝑐 = 12𝑉 − 6 × 10−3A × 1.5 × 103Ω

𝑉𝑐 = 3 𝑉

𝑉0 = − (𝑅𝑓

𝑅𝒊) 𝑉𝑖 𝑉0 = − (

12 𝑘Ω

4 𝑘Ω) × 3 V

𝑉0 = −9 𝑉

mikg;Gf;fl;Liu tpdhtpw;fhd tpilfs;

(1) (a)

……………(1) Gs;spfs;

rupahf njhLj;jpUe;jhy; ……………(1) Gs;spfs;

(b) epWj;jw;fbfhuk; > Ntzpau; ,Lf;fpkhdp > ,yj;jpudpay; juhR ……………(2) Gs;spfs;

(c) P Q / NkypUe;J fPohf ……………(1) Gs;spfs;

• nfhjpePuhtp miwia Kw;whf epug;gpa gpd;dNu ntspNaWk;(tpidj;jpwdhd ntg;gg;gupkhw;wk;)

• xLq;fpa ePu; ,ilA+W ,d;wp Q ,D}L ntspNaWk;

……………(2) Gs;spfs;

(d) khwh ntg;gepiyapy; ngwyhk; vd;gjhy; , nfhz;Ls;s ntg;grf;jp cau;T vd;gjhy;

……………(2) Gs;spfs;

(e) rpwe;j ntg;gj;njhLifia Vw;gLj;j ……………(1) Gs;spfs;

(f) khwh mKf;fj;njhl;b itf;fg;gl;l cauj;ij Fiwj;jy;

……………(1) Gs;spfs;

(g) Kuz;jpir

……………(1) Gs;spfs;

(h)

(1) ……………(1) Gs;spfs; (2) ……………(1) Gs;spfs;

t t

θ θ

(i) 𝑄

𝑡=

𝐾𝐴(𝜃1−𝜃2)

𝑥

……………(2) Gs;spfs;

(j) tsp

……………(1) Gs;spfs;

(k) Mk; ……………(1) Gs;spfs;

Vnddpy; tsp Nkw;fhTif %yk; R+oYf;F ntg;gj;ij flj;Jk;. nghypj;ijupd; mt;thwpy;iy

……………(2) Gs;spfs;

(𝟐𝟎 Gs;spfs;)

fl;Liu tpdhtpw;fhd tpilfs;

(1)

(a)

i)

mOj;jrf;jp ,af;frf;jpahf khWfpd;wJ

… ……………(1) Gs;spfs;

…………………………………………………….…………(1) Gs;spfs;

ii) mOj;jrf;jp ,af;frf;jpahfTk; cuha;Tf;F vjpuhf nra;ag;gl;l NtiyahfTk; khw;wg;gLfpd;wJ

……………(1) Gs;spfs;

…………………………………...……………(1) Gs;spfs;

(b)

i)

F=ma ,l

4.8 x 105 x sin 𝜃 = 4.8 x 104 a ……………(1) Gs;spfs; 0.2 𝑥 10 = 𝑎 𝑎 = 2 𝑚 𝑠−2 ……………(1) Gs;spfs;

ii) ,Uk;Gj;jfl;Lf;Fk; fg;gYf;Fk; ,af;fj;jpd;Nghjhd cuha;Ttpiria Fiwg;gjw;F

……………(1) Gs;spfs;

iii)

V2 = u2 + 2as

0 = 82 + 2a1 x 40 ……………(1) Gs;spfs;

a1= -0.8ms-2 ……………(1) Gs;spfs;

mku;KLfypd; gUkd; = 0.8𝑚𝑠−2

iv) F = ma

F1 =4.8 x 104 x 0.8 ……………(1) Gs;spfs;

= 3.84 x 104 N ……………(1) Gs;spfs;

v) Ff – 4.8x 105 sin 𝜃 = 3.84 x 104 ……………(1) Gs;spfs;

Ff =9.6 x 104 +3.84 x 104 N

= 13.44 x 104 N ……………(1) Gs;spfs;

(c)

i) nghwpKiwr; rf;jpf;Nfhl;ghl;il gad;gLj;jp>

mgh = 1

2mv2

mg 30 sin 𝜃 = 1

2mv12 ……………(1) Gs;spfs;

V12 = 120

V1 = 2√30 ms-1 ……………(1) Gs;spfs;

ii) V2 = u2 + 2as

v22 = 120- 2x 0.8 x 45 ……………(1) Gs;spfs;

V22 = 48 ms-1

V2 = 4√3 ms-1 ……………(1) Gs;spfs;

iii) cUisapy; v =u+at

2√30=2 x t1 ……………(1) Gs;spfs;

t1 =√30 s

,Uk;Gj;jfl;Lf;F v=u+at

4√3 = 2√30 – 0.8 t2

t2 = 5√3 (√10 −2)

2 ……………(1) Gs;spfs;

nkhj;j Neuk; = t1+ 𝑡2

=√30 s + 5√3 (√10 −2)

2

= √3(7√10−10)

2 ……………(1) Gs;spfs;

iv)

……………(1) Gs;spfs;

(d)

i) ,Uk;Gj;jfl;by;

F=ma

T1 - Ff – 4.8 x 105 sin 𝜃 =0

T1 =9.6 x 104 + 13.44 x 104

= 23.04 x 104 ……………(1) Gs;spfs;

cUisapy;>

T2 - 4.8 x 105 sin 𝜃 = 0

T2 =9.6 x 104 N ……………(1) Gs;spfs;

ii) P=Fv ,Uk;Gj;jfl;by;>

P1 = 23.04 x 104 N x 1ms-1

= 23.04 x 104 W ……………(1) Gs;spfs; cUisapy;>

P2 = 9.6 x 104 x 1 ms-1

= 9.6 x 104 W ……………(1) Gs;spfs;

iii) 𝜏 = 𝐹𝑟 → 𝜏𝑚𝑎𝑥 = (𝐹𝑟)max ,Uk;Gj;jfl;by; fg;gy; cs;sNghJ ,Oit cau;T. cUisapy; fg;gy; cs;sNghJRoypapd; Miu cau;T. cUisia te;jilAk;NghJ

4

1 23.04 10 0.5 =

411.52 10 Nm= ……………(1) Gs;spfs;

fk;gp Kw;whf Row;wg;gl;l gpd;>

4

2 9.6 10 0.6 =

45.76 10 Nm= ……………(1) Gs;spfs;

1 2

4

max 11.52 10 Nm

= ……………(1) Gs;spfs;

iv) P x 0.3 = 23.04 x 104 ……………(1) Gs;spfs;

P= 230.4 ×104

3

= 76.8 x 104

=7.6 x 105 W ……………(1) Gs;spfs;

(𝟑𝟎 Gs;spfs;)

****************