Chapter # 4
Forces
Solved Examples 1.
Sol.
Suppose the exact charge neutrality does not hold in a world and the electron has a charge 1% less in magnitude than the proton. Calculate the Coulomb force acting between two blocks of iron each of mass 1 kg separated by a distance of 1 m. Number of protons in an iron atom = 26 and 58 kg of iron contains 6 × 1026 atins. Each atom of iron will have a net positive charge 26 × 0.01 × 1.6 × 10–19 C on it in the assumed world. The total positive charge on a 1 kg block would be
6 10 26 × 26 × 1.6 × 10–21 C 58 = 4.3 × 105 X. The Coulomb force between the two blocks is =
1 4 0
q1q2 r2
=
9.0 10 9 N m 2 / C 2 ( 4.3 10 5 C)2 (1m)2
= 9 × 10–9 × 18.49 × 10 10 N = 1.7 × 10–21 N. A tremendous force indeed !
Worked out Examples 1.
Figure shows two hydrogen atoms. Show on a separate diagram all the electric forces acting on different particles of the system.
Sol.
Each particle exerts electric forces on the remaining three particles. Thus there exist 4 × 3 = 12 forces in all. Figure shows them.
2.
Figure shows two rods each of length l placed side by side , with their facing ends separated by a distance a . Charges +q, –q reside on the rods as shown. Calculate the electric force on the rod, A due to the rod B. Discuss the case when l >>a, a>>l.
Sol.
The force on the rod A due to the change +q of the rod B
q2 =
4 0 (l a)
2
q2 4 0 a 2
towards right . The force on this rod due to the charge –q
q2 =
4 0 (2l a)2
q2 4 0 ( l a)2
towards right . The resultant force on the rod is manishkumarphysics.in
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Chapter # 4
Forces
1 2 1 2 2 2 towards right. (l a ) (2l a) a If l >> a, the last two terms in the square brackets are negligible as compared to the first term. Then
q2 F= 4 0
q2
F
4 0 a 2
If a >> l
q2 1 2 1 2 2 2 0 4 0 a a a Two neutral objects placed far away exert only negligible force on each other but when they are placed closer they may exert appreciable force. F
3.
Calculate the ratio of electric to gravitational force between two electrons.
e2 Sol.
The electric force =
4 0 r 2
and the gravitational force =
G(me )2 r2
e2 The ratio is
9 10 9 =
4 0 G(me )2 N m2 C
2
(1.6 10 19 C)2
Nm 6.67 10 11 2
2
(9.110
31
= 4.17 × 1042.
kg)
2
kg
QUESTIONS FOR SHORT ANSWERS 1.
A body of mass m is placed on a table . The earth is pulling the body with a force mg. Taking this force to be the action , what is the reaction?
2.
A boy is sitting on a chair placed on the floor of a room. Write as many action-reaction pairs of forces as you can
3.
A lawyer alleges in court that the police has forced his client to issue a statement of confession. What kind of force is this?
4.
When you hold a pen and write on your notebook, what kind of force is exerted by you on the pen? By the pen on the notebook? By you on the notebook ?
5.
Is it true that the reaction of a gravitational force is always gravitational, of an electromagnetic force is always electromagnetic and so on ?
6.
Suppose the magnitude of Nuclear force between two protons varies with the distance between them as shown in figure. Estimate the ratio “Nuclear force / Coulomb force” for (a) x = 8 fm (b) = 4 fm, (c) x = 2 fm, (d) x = 1 fm (1fm = 10–15 m.)
7.
List all the forces acting on the block B in figure. manishkumarphysics.in
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Chapter # 4
Forces
8.
List all the forces acting on (a) the pulley A, (b) the boy and (c) the block C in figure.
9.
Figure shows a boy pulling a wagon on a road. List as many forces as you can which are relevant with this figure . Find the pairs of forces connected by Newton’s third law of motion.
10.
Figure shows a cart . Complete the table shown below.
Force on
Force by
Nature of the force
Cart
1 2 3 :
Horse
1 2 3 :
Driver
1 manishkumarphysics.in 2 3 :
Direction
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Chapter # 4
Forces
Objective I 1.
When Nells Bohar shook hand with Werner Heisenberg, what kind of force they exerted ?
tc uhYl cksj] ouZj gkbtucxZ ls gkFk feykrk gS rks muds e/; dkSulk cy yxrk gS & (a) Gravitational (a) xq:Roh; 2.
(b*) Electromagnetic (b*) fo|qr&pqEcdh;
(c) Nuclear (c) ukfHkdh;
(d) Weak (d) {kh.k
Let E,G and N represents the magnitude of electromagnetic, gravitional and nuclear forces between two electrons at a given separation . Then
ekukfd fdlh fuf’pr nwjh ij fLFkr] nks bysDVªkWuksa ds e/; yxus okys fo|qr pqEcdh;] xq:Roh; rfkk ukfHkdh; cyksa ds ifjek.k Øe'k% E,G rFkk N gS] rks & (a) N < E < G 3.
(b) E > N > G
(c) G > N > E
(d*) E > G > N
The sum of all electromagnetic forces between different particles of a system of charged particles is zero.
vkosf'kr d.kska ds fudk; ds fofHkUu d.kksa ds e/; yxusokys fo|qr&pqEcdh; cyksa dk ;ksx 'kwU; gksxk & (a) Only if all the particles are positively charged.
dsoy ;fn fo|qr&pqEcdh; cyksa dk ;ksx 'kwU; gksxk& (b) Only if all the particles are negatively charged.
dsoy ;fn leLr d.k _.kkosf'kr gSA (c) Only if half the particles are positively charged and half are negatively charged.
dsoy ;fn vk/ks d.k /kukosf'kr rFkk vk/ks d.k _.kkosf'kr gSA (d*) irrespective of the signs of the charges.
vkos'kksa ds fpUg ij fuHkZj ugha djrk gSA 4.
A 60 kg man pushes a 40 kg man by a force of 60 N. The 40 kg man has pushed the other man with a force. 60 fdxzk nzO;eku dk ,d O;fDr 40 fdxzk- nzO;eku okys ;fDr dks 60 N cy ls /kDdk nsrk gSA 40 fdxzk nzO;eku dk
O;fDrnwljs dks fuEu cy ls /kdsysxk & Sol.
(a) 40N (b) 0 (c*) 60N Due to action reaction pair they will be equal in magnitude.
(d) 20N
Objective II 1.
A neutron exerts a force on a proton which is
,d U;wVªkWu fdlh izksVkWu ij tks cy yxkrk gS] og gS & (a*) gravitional (a*) xq:Roh; 2.
(b) electromagnetic (b) fo|qr&pqEcdh;
(c*) nuclear (c*) ukfHkdh;
(d) weak (d) {kh.k
(c*) nuclear (c*) ukfHkdh;
(d) weak (d) {kh.k
A proton exerts a force on a proton which is
dksbZ izksVkWu] fdlh vU; izksVkWu ij tks cy yxkrk gS] og gS & (a*) gravitional (a*) xq:Roh; 3.
(b*) electromagnetic (b) fo|qr&pqEcdh;
Mark the correct statements :
lR; dFku pqfu;s & (a) The nuclear force between two protons is always greater than the electromagnetic force between them.
nks izksVkWuksa ds e/; yxus okyk ukfHkdh; cy lnSo muds e/; yxus okys fo|qr&pqEcdh; cyls vf/kd gksrk gSA (b*) The electromagnetic force between two protons is always greater than the gravitional force between them.
nks izksVkWuksa ds e/; yxus okyk fo|qr&pqEcdh; cy lnSo muds e/; yxus okys xq:Roh; cy ls vf/kd gksrk gSA (c*) The gravitional force between two protons may be greater than the nuclear force between them.
nks izksVkWuksa ds ds e/; yxus okyk xq:Roh; cy] muds e/; yxus okys ukfHkdh; cy ls vf/kd gks ldrk gsA (d*) The electromagnetic force between two protons may be greater than the nuclear force acting between them.
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Chapter # 4
Forces
nks izksVkWuksa ds e/; yxus okyk fo|qr pqEcdh; cy muds e/; yxusokys ukfHkdh; cy ls vf/kd gks ldrk gSA 4.
If all matter were made of electrically neutral particles such as neutrons,
;fn leLr inkFkZ oS|qr mnklkhu d.kksa tSls U;wVªkWuksa ls cuk gksrk & (a*) there would be no force of friction. (c*) it would not be possible to sit on a chair (a*) rks ogk¡ dksbZ ?k"kZ.k cy ugha gksrkA (c*) rks ogk¡ dqlhZ ij cSBuk laHko ugha gksrkA 5.
(b*) there would be no tension in the string (d) the earth could not move around the sun. (b*) rks ogk¡ Mksjh esa ruko ugha gksrkA (d) rks i`Foh lw;Z ds pkjksa vksj xfr ugha djrhA
Which of the following systems may be adequately described by classical physics ?
fuEu esa ls dkSuls fudk; Bhd fpj lEer ;kaf[kdh ds varxZr vkrs gS & (a*) motion of a cricket ball (c) a hydrogen ato (a*) fØdsV dh xsan dh xfr (c) gkbMªkstu ijek.kq 6.
(b*) motin of a dust particle (d) a neutron changing to a proton. (b*) /kwy ds d.k dh xfr (d) izksVkWu esa ifjofrZr gksrk gqvk ,d U;wVªkWu
The two ends of a spring are displaced along the length of the spring. All displacement have equal magnitudes. In which case or cases the tention or compression in the spring will have a maximum magnitude ?
fdlh fLizax ds nksuksa fljs fLizax dh yEckbZ ds vuqfn'k foLFkkfir fd;s x;s gsA leLr foLFkkiu leku ifjek.k ds gSA fdl fLFkfr esa ;k fLfkfr;ksa esa fLizax esa ruko ;k laihMu dk ifjek.k vf/kdre gS & (a*) the right end is displaced toward right and the left end towards left.
nk;ka fljk nk;h vksj rFkk ck;ka fljk ck;ha vksj foLFkkfir fd;k tk;sA (b) both ends are displaced towards right.
nksuksa fljs nk;ha vksj foLFkkfir fd;s tk;sA (c) both ends are displaced towards left.
nksuksa fljs ck;ha vksj foLFkkfir fd;s tk;sA (d*) the right end is displaced towards left and the left end towards right.
nk;ka fljks ck;ha vksj rFkkck;ka fljk nmk;ha vksj foLFkkfir fd;k tk;sA 7.
Action and reaction
fØ;k rFkk izfrfØ;k & (a*) act on two different objects (c*) have opposite directions (a*) nks fHkUu&fHkUu oLrqvksa ij yxrh (c*) dh fn'kk,sa foijhr gksrh gSA
gSA
(b*) have equal magnitude (d*) have resultant zero. (b*) ds ifjek.k ,d leku gksrs (d*) dk ifj.kkeh 'kwU; gksrk gSA
gSA
Exercises 1.
The gravitational force acting on a particle of 1 g due to a similar particle is equal to 6.67 × 10 –17N. Calculate the separation between the particles. 1 xzke nzO;eku okys d.k ij ,sls gh ,d vU; d.k }kjk yxus okyk xq:Roh; cy 6.67 × 10–17N U;wVu gSA d.kksa ds
e/; nwjh dh x.kuk dhft;sA [Ans : 1m] 2.
Calculate the force with which you attract the earth.
i`Foh ds }kjk vki ij yxus okys dk"kZ.k cy dh x.kuk dhft;sA 3.
At what distance should two charges , each equal to 1C be placed so that the force between them equals your weight ? leku ifjek.k 1 C okys nks vkos'kksa dks fdruh nwj j[kktk;s fdmuds e/; yxus okyk cy] vkids Hkkj ds cjkcj gS \
4.
Two spherical bodies, each of mass 50 kg, are placed at a sepration of 20 cm. Equal charges are placed on the bodies and it is found that the force of Coulomb repulsion equals the gravitational attraction in magnitude of the charge placed on either body. nks xksykdkj o0Lrvksa] ¼izR;sd nzO;eku 50 fdxzk gS½ dks 20 lseh nwj j[kk x;k gSAoLrqvksa ij leku vkos'k j[ks x;s gS
rFkk ;g izsf{kr fd;k x;k gS fd dwykeh; fod"kZ.k cy rFkk xq:Roh; cy ds ifjek.k cjkcj gSA fdlh Hkh oLrq ij j[ks x;s vkos'k dk ifjek.k Kkr dhft;sA manishkumarphysics.in
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Chapter # 4
Forces
[Ans : 4.3 × 10–9C] 5.
A monkey is sitting on a tree limb. The limb exerts a normal force of 48N and a fractional force of 20N. Find the magnitude of the total force exerted by the limb on the monkey. ,d cUnj isM+ dh Mkyh ij cSBk gSAMkyh ds }kjk yxk;k x;k vfHkyEcor~ cy 48N rFkk ?k"kZ.k cy 20 N gSA Mkyh ds
}kjk cUnj ij yxk;s x;s dqy cy dh x.kuk dhft;sA [Ans : 52N] 6.
A body builder exerts a force of 150N against a bullworker and compresses it by 20cm. Calculate the spring constant of the spring in the bullworker. ,d igyoku cqyodZj ij 150 N cy yxkdkj bldks 20 lseh lEihfMr dj nsrk gSA cqyodZj esa yxh gqbZ fLiazx dk
fLizax fu;rkad Kkr dhft;sA [Ans : 750 N/M] 7.
A satellite is projected vertically upwards from an earth station. At what height above the earth’s surface will the force on the satellite due to the earth be reduced to half its value at the earth station? (Radius of the earth is 6400 km.)
i`Foh dh lrg ij fLFkr LVs'ku ls m/okZ/kj Åij dh vksj ,d mixzg iz{ksfir fd;kx;k gSA i`Foh dh lrg ls fdl Å¡pkbz ij i`Foh ds dkj.k yxus okyk cy] bl LVs'ku ij i`Foh ds dkj.k cy dk vk/kkj jg tk;sx \ (i`Foh dh f=kT;k 6400 fdeh gS) [Ans : 2650 km] 8.
Two charged particles placed at a separation of 20 cm exert 20N of Coulomb force on each other. What will be the force if the separation is increased to 25 cm ? 20 lseh nwjh ij fLFkr nks vkos' k ijLij 20 N dwy keh; cy yxkrs gSA ;fn buds e/; nwjh c<+kdj 25 lseh dj nh
tk;s rks cy fdruk gks tk;sxk \ [Ans : 13N] 9.
The force with which the earth attracts an objects is called the weight of the object. Calculate the weight of the moon from the following data : The universal constant of gravitation G = 6.67 × 10 –11 N– m 2/kg2, mass of the moon = 7.36 × 1022 kg, mass of the earth = 6 × 1024 kg, and the distance between the earth and the moon = 3.8 × 105 km.
fdlh oLrq dks i`Foh ftl cy ls vkdf"kZr djrh gSA og ml oLrq dk Hkkj dgykrk gSA fuEufyf[kr vkadM+ks ds vk/ kkj ij pUnzek ds Hkkj dh x.kuk dhft;s % xq:Rokd"kZ.k dk lkoZf=kd fu;rkad G = 6.67 × 10–11 N–m 2/kg2, pUnzek dk nz;eku = 7.36 × 1022 kg, i`Foh dk nzO;eku = 6 × 1024 kg, i`foh ,oa pUnzek ds chp dh nwjh = 3.8 × 105 km. [Ans : 2 × 1020N] 10.
Find the ratio of the magnitude of the electric force to the gravitational force between two protons.
nks izksVkWuksa ds e/; yxus okys oS|qr cy rFkk xq:Roh; cy dk vuqikr Kkr dhft;sA 11.
[Ans : 1.24 × 1036] The average separation between the proton and the electron in a hydrogen atom in ground state is 5.3 × 10–11m. gkbMªkstu ijek.kq dh ewy voLFkk esa izksVkWu rFkk bysDVªkWu ds e/; vkSlrnwjh 5.3 × 10–11 eh- gSA (a) Calculate the Coulomb force between then at the separation
bl nwjh ij nksuksa ds e/; dwykeh; cy dh x.kuk dhft;sA (b) When the atom goes into its first excited state the average separation between the proton & electron process to four times its value in the ground state what is the coulomb force in this state.
tc ijek.kq izFke mÙksftr ÅtkZ Lrj esa tkrk gS rks izksVkWu rFkk bysDVªkWu ds e/; vkSlr nwjh] ewy ÅtkZ voLFkk dhnwjh dh pkj xquh gks tkrh gSA bl voLFkk esa dwykeh; cy dk eku fdruk gS \ [Ans : (a) 8.2 × 10–8 N, (b) 5.1 × 10–9 N] 12.
The geostationary orbit of the earth is at a distance of about 36000 km from the earth’s surface. Find the weight of a 120-kg equipment placed in a geostationary satellite. The radius of the earth is 6400 km. i`Foh dh Hk&LFkk;h d{kk dh i`Foh dh lrg ls nwjh yxHkx 36000 fdeh gSA Hkw&LFkk;h mixzg esa j[ks gq, 120 fdxzk nzO;eku ds midj.kdk Hkkj Kkr dhft;sA i`Foh dh f=kT;k 6400 fdeh gSA [Ans : 27N] manishkumarphysics.in
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