alp solutions wpe physics hindi

RESONANCE WORK, POWER & ENERGY - 1

TOPIC : 'kf ] dk;Z ,oa tkZ (WORK, POWER & ENERGY)1. W = sd.F = )j5it3( . (4t dt i )

= 2

0

2 dtt12=

3t12

20

3 = 32 J

2. W vf/kd re d s fy, ; dxdW

= 0 ;

i.e. F(x) = 0 x = , x = 0d = d s fy,] fd ;k x;k d k;Z vf/kd re gSA

oSd fYid gy :ck cy o foLFkkiu ,d gh fn'kk esa gSA d k;Z /kukRed gksxkA;g yxkrkj gksxk o vf/kd re foLFkkiu ij vf/kd re gksxkA

3. pky 0 ls V djus esa dk;Z

W1 = 21

mV2

pky V ls 2V djus esa dk;Z

W2 = 21

m (2V)2 21

mV2 = 21

3 mV2

21

WW

= 31

4. CykWd ij dk;Z tkZ es; yxkus ij

WF + WS = 0

F 21

k2 = 0 = kF2

;k

vr% dk;ZA = F = kF2 2

5. fLizax ds eqDr fljs ds ra=k esa iF`oh ds lkis{k tM+Roh;] xqVds dk izkjfEHkd osx 3 m/s cka;h vksj gS o fLizax fcuk [khapk gSA

3m/s 4kg

4kg

izkjfEHkd voLFkk

vf/kdre foLrkj voLFkk

A

PHYSICS SOLUTIONSADVANCE LEVEL PROBLEMS

TARGET : JEE (IITs)


izkjfEHkd o vf/kdre foLrkj dh voLFkk esa tkZ laj{k.k djus ij

21

mv2 = 21

kA2 or A = km

v = 3100004

= 6cm.

6. dk;Z : = Mgh1 + Mgh2 + Mgh3 + 1 Mg1 + 2 Mg2 + 3Mg3 = Mg (h1 + h2 + h3) + Mg (11 + 22 + 33) = Mg (8 + 0.2 + 0.4 + 0.4) = 90 J

7. tkZ laj{k.k ls

K.E. + P.E. = E ;k K.E. = E 21

kx2

K.E. at x = kE2

is

E 21

k

kE2

= 0

x = kE2

ij d.k dh pky 'kwU; gSA

8. pSu ds ijh fljs }kjk 8

, nwjh fxjus ds ckn pSu dh pky gS -

v = 8g2

=

2g

.

est ds ij psu dk nzO;eku 87

M. gSA

psu dk laosx gS

87

M 2g

= 167

M g

9. ekuk v fuEure fLFkfr ij B dh pky gS] fuEure fLFkfr ij A dh pky 2v gSA tkZ laj{k.k ls &

21

m (2v)2 + 21

mv2 = mg (2) + mg.

gy djus ij ge ikrs gSa - v = 5g6

.

10. ekuk vUr esa ikuh ds lrg dh pkbZ h gSA


a2h = a . 2a

. 2a

; h = 4a

nzO;eku d sUnz uhps vk;sxk a

8a

4a

= a 8a3

= 8a5

vr% xq:Ro }kjk fd;k x;k dk;Z = mg 8a5

11. ;g izsf{kr fd;k tk ldrk gS fd cy F }kjk d.k dks nh xbZ 'kfDr gS -P = Fv = K.

'kfDr fu;r gSA vr% le; t esa cy }kjk fd;k x;k dk;Z gS -W = Pt = Kt

12. cy }kjk le; t = 0 ls t = t sec. rd fd;k x;k dk;Z xzkQ ds uhps Nk;kafdr {ks=kQy }kjk fn;k tkrk gSAvr% tSls&tSls t c


= v1 = 8.5 m/secblh izd kj 6 d ksp d s fy, K6mgv = k8mgv2

v2 = 86

20 = 43

20 = 15 m/sec

16. ekuk F og cy gS ftlds }kjk vkneh xqVds dks [khaprk gSA Fv = 500 F = 50 N

(F - mg) v = 100gy djus ij m = 4 kg

17. fcUnq 'C' ij fLFkfrt tkZ U;wure gS vr% ;g fcUnq LFkk;h lkE;koLFkk esa gSAE ls F rd


3. (a) xfr izkjEHk gksus ds fy,

4mg5 k

> smg or 5k > 4s

(b)

xqVds dh vfUre fLFkfr ij fLizax esa foLrkj vf/kdre gS ,oa xqVds dh pky v = 0 gSA vr% xqVds dks izkjfEHkd ls vfUre fLFkfrrd ys tkus esa fd;k x;k dqy dk;Z

W = P }kjk fd;k x;k dk;Z + fLizax cy F }kjk fd;k x;k dk;Z + ?k"kZ.k }kjk fd;k x;k dk;Z = K = 0

= P x x

0

3 dx.Kx kmgx = 4mg5 k

x 4

Kx4 kmgx = 0

gy djus ij x = 3/1

KKmg

4. ftl {k.k foLrkj vf/kdre gS] xqVds dh pky 'kwU; gks tkrh gSAfudk; ij dk;Z tkZ izes; yxkus ij

0 21

. mv2 = Wg + Ws

21

. 2.4 = 2.10 . x 2

1 . 100 . x2

gy djus ij x = m513

5. A rFkk B e/; dk;Z mtkZ izes; ls

3m

3m

37

21

mVB2 21

mVA2 = Wxq: Ro + W?k"kZ.k

21

mVB2 21

m (136) = mg(3 + 3 sin 37) mg cos 37 x 3

2

V2B 2

136 = 48 12 VB = 4 m/s


6. vf/kdre fQlyu dh fLFkfr rc mRiUu gksrh gS tc fLizax vf/kdre lEihfMr gksrh gSA bl {k.k fLaizx }kjk vkjksfir cyvf/kdre gS rFkk fudk; dk Roj.k Hkh vf/kdre gSA vr% bl fLFkfr esa vko';d ?k"kZ.k cy vf/kdre gSAdk;Z mtkZ izes; ls

21 (M + m) V2 = 2

1 Kx

m2 x

m =

KV)mM( 2

ijh CykWd ds fy, am =

mMkxm

ijh CykWd ij cy] ?k"kZ.k cy }kjk fn;k tkrk gSA

vr% mg > mMm.kxm

lhekar eku ds fy, V = g k

mM

ekuksa ds iz;ksx ls Vvf/kdre

= 20 cm/s

7. pky vf/kdre gS tc Roj.k U;wure gSA tc xqVds dh pky vf/kdre gSrc ekuk xqVds dk foLFkkiu x0 gSAlkE;koLFkk ij ur ry ds vuqfn'k xqVds ij U;wVu dk fu;e yxkus ij

mg sin = mg cos + kx0 ..................(1)izkjfEHkd o vfUre fLFkfr ds e/; xqVds ij dk;Z tkZ izes; yxkus ij

Kf = Ki + mg x0 sin 21

kx02 mg x0 cos ...........(2)(1) o (2) dks gy djus ij

Vmax

= (sin cos) g km

Ans. Vmax

= (sin cos) g Km

8. (i) osx vf/kdre gksxk tc ifj.kkeh cy = 0

k.x = N = mg x = mgk

d k;Z t kZ izes; lsW

s + W f = K

kmg

mgkmgk

21

kmg2k

21 22

=

21

mv2

gy djus ij,

v = kmg .

(ii) tc d.k dk osx 'kwU; gS rks ekuk fLizax esa foLrkj '

x

' gSA

12

k 22 mg

k

= mg2 mg

kx

+

12

k

x2


22 2 2m g

k = 2

2 2 2m gk

+ x mg + 12

k x2 x2 mg

kx

= 0

x = 0 (izkfrd yEckbZ ij) ;k x = 2 mgk

tc fLiazx esa laihMu 2 mg

k vFkkZr~ izkjEHk esa

blfy, izkfrd yEckbZ ij osx 'kwU; gSA fLizax cy Hkh 'kwU; gSA xqVdk okil ugha ykSVsxk vkSj bldk osx cka;h vksj gSA

9. (a) tc F = 0 gks rks d.k lkE;oLFkk esa gksrk gSA

x (3x 2) = 0 x = 0 and x = 32

m

d.k x = 0 o x = 32

ij lkE;koLFkk esa gSA

(b)

x = 0 ij d.k LFkk;h lkE;koLFkk esa o x = 32ehVj ij vLFkk;h lkE;koLFkk esa gSA

pwafd x = 0 ij 0dxdF

0dx

Ud2

2

vkSj x = 32

m ij 0dxdF

0

dxUd2

2

(c) d.k dk nh xbZ U;wure pky bl izdkj gksuh pkfg, rkfd ;g Bhd x = 32

ij igqps ogk ls ;g x = 0 rd Lor%

igqp tk;sxkA

21

mv2 = 3/2

4

dxF = dx)2x3(x

3/2

4

= 27

1300;k v = 27

2600m/s

10. F = x

U

i yU

j = [6 i ] + [8] j = 6 i + 8 j

a

= 3 i + 4 j Roj.k dh fn'kk

2a

2j4i3

u

ds leku gSA

| a | = 5 | u | = 5/2pwafd u

rFkk a

,d gh fn'kk esa gS] vr% d.k ljy js[kk ds vuqfn'k xfr djsxkA

S = 25

2 + 21

5 22 = 5 + 10 = 15 m.

11. d k;Z t kZ izes; ls

21

mV2 - 0 = 5

0dx )x410(

V = 10m/s bl {k.k cy = (10 + 20) = 30 Nrkf{k.kd 'kfDr = 30 10 = 300W

alp solutions wpe physics hindi

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