HISSAN QUESTIONS AND ANSWERS SHORT QUESTIONS AND ANSWERS (HSEB)
1.
Can an object with contant acce!e"ation "e#e"e it $i"ection% E&'!ain.
Ans. Yes, the direction of a body can change, when its acceleration is constant. For example if the body is moving on circular path with a constant speed, the direction of velocity at any point is given by the tangent drawn at that point. Hence, the direction of velocity changes at every point. However, the acceleration of the body is always towards the centre with its constant magnitude.
.
I the *n o+ehow co!!a'e$ to o"+ a b!ac, ho!e- what eect wo*!$ thi e#ent ha#e on the o"bit o the ea"th%
Ans. Ans. If the sun collapsed into a black hole, it would have the same mass but smaller radius. ince, the gravitational attraction of the sun on the earth does not depend on the sun!s radius, the earth!s orbit would not be affected. However, according to our understanding understanding,, sun cannot be collapsed to form black hole.
.
A bo$/ i +o#in0 in a ci"c*!a" 'ath with contant 'ee$. I thi +otion a i+'!e ha"+onic% E&'!ain.
Ans. A body is moving in a circular path with constant speed is called circular motion. And the pro"ection of this motion in fixed line is called simple harmonic motion. #hen a body is moving in a circular path with constant speed, the magnitude of velocity is constant. ince, in a H$ velocity cannot be constant, the motion of the body moving in a circular path with constant speed is not simple harmonic motion.
.
What i the $ie"ence between acc*"ate an$ '"ecie +ea*"e+ent%
Ans. Accurate measure measurement ment : It is the agreement of the result of a measurement with the true value of the measured %uantity. If the measurement of a dimension of a part approximates very closely to the true value of that dimension, it is said to be accurate. &hus the term accurate denotes the closeness of the measured value with the true value. Precise measure measurement ment : It
is the repeatability of the measuring process. It refers to the group of measurements for the same sa me characteristics taken under identical conditions. It indicates to what extent the identically performed measurements agree with each other. If the measurement is not precise the results vary about the mean.
2.
I the *n o+ehow co!!a'e$ to o"+ a b!ac, ho!e- what eect wo*!$ thi e#ent ha#e on the o"bit o the ea"th%
Ans. If the sun collapsed into a black hole, it would have the same mass but smaller radius. ince, the gravitational attraction of the sun on the earth does not depend on the sun!s radius, the earth!s orbit
would not be affected. However, according to our understanding, sun cannot be collapsed to form black hole.
3.
D*"in0 '"e0nanc/- wo+en oten $e#e!o' bac, 'ain "o+ !eanin0 bac,wa"$ whi!e wa!,in0. Wh/ $o the/ ha#e to wa!, thi wa/%
Ans' (uring pregnancy, the centre of gravity lies front part of the body. For the stable e%uilibrium, the vertical line of ). *. must pass through the base. For this reason, pregnant women lean backward. If she does not bend backward, the ). *. falls outside and it will be difficult to walk. o, during pregnancy, women have lean backward while walking.
4.
I the o"ce o 0"a#it/ act on a!! bo$ie in '"o'o"tion to thei" +ae- wh/ $oe not hea#/ bo$/ a!! ate" than a !i0ht bo$/%
Ans. &he acceleration due to gravity of a body is, g+ *$ - It shows that acceleration due to gravity is independent of mass of the body. &herefore, all masses fall with the same rapidity provided air resistance is neglected.
5.
E&'!ain wh/ o!$ie" a"e o"$e"e$ to b"ea, te' whi!e c"oin0 a b"i$0e%
Ans. oldiers are ordered to break their steps while crossing the bridge because when they march in steps the fre%uency of marching coincides with the natural fre%uency of the bridge. In this case, resonance will occur in the bridge and begins to vibrate with maximum amplitude which may cause the destruction of the bridge. &o avoid such a destruction of the bridge soldiers are ordered to break their steps while crossing it.
(HISSAN)
6.
In a 0i#en e7*ation8 / 9 ain(:t ; ,&)- in$ the $i+enion o : an$ ,.
Ans. ince, /0t 1 kx2 is an angle, it is a dimensionless %uantity. It means that 0t as well as kx is dimensionless. (imensional formula of 0t + 3$ 454 &46 + 7 8r, 306 + 73t6 8r, 306 + 73$ 454 &6 8r, 306 + 3&976
1<. A 'e"on wa!,in0 on the "oa$ ho!$ hi *+b"e!!a at o+e an0!e with the #e"tica! when the "ain i a!!in0 #e"tica!!/ $ownwa"$. Wh/%
Ans. #hen the man moves through the rain falling vertically downwards, the rain drops appear to fall in a direction inclined to the vertical. o, as to protect himself from the rain, he holds the umbrella inclined to the vertical in the direction of relative velocity of the rain with respect to him.
11. What 'h/ica! 'heno+enon i the"e that a b!ac, who!e ha hi0h 0"a#it/% Ans. A black hole is formed due to the death of star of mass $, if it is contracted within the radius given by, - :H + *$c, where * represents gravitational constant and c represents the velocity of light. In this case radius is highly contracted which causes high gravity as gravity is inversely proportional to the radius.
1. I A 9 =i > 3j an$ B 9 i ; j- in$ the an0!e between A an$ B. Ans.
A + 9i ; <" : + i 1 <"
5et, = be the angle between two vectors, then, )os= + A+
A . B AB
√ (− 2 ) + 3
2
+
−3 ¿
:+
+
2
2 + ¿ √ ❑
√ 13 √ 13
A.: + /9i ; <"2./ i 1 <"2 + 9>9? + 97< @ow, )os= +
− 13
√ 13 . √ 13
+ 97
+ 7B4
1. What i a b!ac, ho!e% Ans. A black hole is a region of space9time from which nothing, not even light, can escape. &he theory of general relativity predicts that a sufficiently compact mass will deform space9time to form a black hole. Around a black hole there is a mathematically defined surface called an event horiCon that marks the point of no return. It is called DblackD because it absorbs all the light that hits the horiCon, reflecting nothing, "ust like a perfect black body in thermodynamics. Euantum mechanics predicts that black holes emit radiation like a black body with a finite temperature. &his temperature is
inversely proportional to the mass of the black hole, making it difficult to observe this radiation for black holes of stellar mass or greater.
1. Die"entiate between ca!a" '"o$*ct an$ #ecto" '"o$*ct o two #ecto". Ans. calar product /dot product2 7. If the product of two vectors is a scalar %uantity, then such an operation is called the scalar product. . calar product of two vectors follows commutative law. <. calar product of two e%ual is s%uare of the magnitude of either vector.i.e. A.A+ A ector product /cross product2 7. If the product of two vectors is a vector %uantity, then such an operation is called vector product. . ector product of two vectors does not follow commutative law. <. ector product of two e%ual vector is Cero.
12. What ha''en to the #a!*e o ti+e 'e"io$ it !en0th i t"i'!e$% Ans. &he time period of simple pendulum is given by, & + G
√
l g
#hen is length is tripled, &ime period becomes, &! + G
√
3l
g
+
√ 3
G
+
√ 3
&
l g
Hence, time period increases by √ 3 times.
13. To +a&i+i?e the +o+ent o ine"tia o a !/ whee! whi!e +ini+i?in0 it wei0ht- what ha'e an$ $it"ib*tion o +a ho*!$ it ha#e% E&'!ain.
Ans. In order to maximiCe the moment of inertia, most of the mass should be concentrated at the rim, as moment of inertia, I + mr . (ue to large value of moment of inertia, angular velocity changes slightly which helps in maintaining uniform rotational motion.
14. What a"e the $i+enion o contant A an$ B
A λ
in the 0i#en e7*ation @ 9
>
B λ
whe"e @ i the "e"acti#e in$e& o a +e$i*+ an$ i the wa#e!en0th o "a$iation.
Ans. (imensional formula of ! + 3$ 454 &46 (imensional formula of ! + 3$45&46 &he dimension formula of + (imensional formula of A 8r, 3$454 &46 + A3$ 45&46 8r, 3A6 + 356 imilarly, dimensional formula of + (imensional formula of : 8r, 3$454 &46 + :3$45 &46 8r, 3:6 + 356
15. The
'ee$ o a bo$/ in a ci"c!e i contant o" contant cent"i'eta! o"ce- howe#e" the
acce!e"ation i not ?e"o. E&'!ain wh/.
Ans. if the body is moving on circular path with a constant speed, the direction of velocity at any point is given by the tangent drawn at that point. Hence, the direction of velocity changes at every point. o, the acceleration of the body is not Cero.
16. Wh/ ho*!$ the an0*!a" $i'!ace+ent o a i+'!e 'en$*!*+ not e&cee$ "a$ian% Ans. &he restoring force tending to bring the pendulum to its mean position is mgsin at the formula & + G
√
l g
θ . In arriving
, we take sin θ J θ i. e. restoring force + mg θ . For large
values of θ , sin θ K θ . &herefore, the restoring force decreases from mg As a result, the pendulum takes a longer time to complete one vibration.
θ to mgsin θ .
h
<. in$ the $i+enion o '!anc, contant h "o+ the 0i#en e7*ation- 9 p Ans. &he given e%uation is, +
h p
8r, h + p @ow, (imension of planck!s constant is, 3h6 + (imension of momentum /p2 x (imension of wavelength / 2 + 3$5&9763$45&46
.
+ 3$5 &976
1. Wh/ a"tiicia! ate!!ite $oe not a!! towa"$ the ea"th *"ace- a!tho*0h the/ a"e ,e't in the 0"a#itationa! ie!
%$Ans. &hough satellite is continuously attracted towards the centre of earth, but it does not fall on to the earth. It is because the gravitational attraction of earth provides necessary centripetal force to the satellite for its orbital motion around the earth.
. owe" 'a"t o a boat i +a$e hea#/. What i it a$#anta0e% Ans. &he heavy and larger base makes the boat to remain in more stable e%uilibrium as it lowers the centre of gravity of the system. As the centre of gravity is low, more will be the stability of it. Hence, the lower part of a boat is made heavy to prevent from destruction.
. Can a co+'onent o #ecto" be 0"eate" than #ecto" ite!% E&'!ain. Ans. @o, the component of a vector cannot be greater than vector itself. 5et, - be the vector and -cos= and -sin= are its component. ince, the value of cos= and sin= lies between 97 to ;7 /cannot be greater than 72, component of vector cannot be greater than vector itself
.
Whe"e $oe a bo$/ 0o when it i $"o''e$ into a t*nne! that 'enet"ate the ea"th "o+ it cent"e%
Ans. &he body remains at the centre of the earth because at the centre the time period of an ob"ect is infinity as acceleration due to gravity is Cero. i.e. & + G
√
& + G
√
l g
l 0
+L
2. A ba!!et $ance" t"etche he" han$ when he want to co+e at "et- wh/% Ans. Ans' A ballet dancer stretches her arms to increase her moment of inertia. As moment of inertia increases, angular velocity decreases and the dancer can reduce her motion.
3.
Show that the o!!owin0 'ai" o 'h/ica! 7*antitie ha#e i$entica! $i+enion. (i) o+ent*+ an$ i+'*!e (ii) To"7*e an$ ene"0/.
Ans. /i2 $omentum and Impulse $omentum + mass x velocity (imension of momentum+ (im of mass x (im of velocity
+ 3$635&976 + 3$5&976 Again, Impulse + force x time (imension of impulse + (im of force x (im of time + 3$5&963&6 + 3$5&976 Hence, dimension of momentum + dimension of impulse /ii2 &or%ue and Mnergy &or%ue + force x distance (imension of tor%ue + (im of force x (im of distance + 3$5&96356 + 3$5&96 Again, (imension of energy + 3$5 &96 Hence, dimension of tor%ue + dimension of energy
4. A
b*c,et- *!! o wate" can be whi"!e$ in a #e"tica! ci"c!e witho*t !ettin0 the wate" a!!
$own. E&'!ain. How that 'oib!e%
Ans. #hen a filled with water is rotated in a vertical circle, it experiences different centrifugal forces at different positions. #hen it reaches at its highest position, the centrifugal force /mv r2 acts vertically upward which balances the weight of water with bucket /mv r Nmg2. hence, the water does not fall down from the bucket.
5. I it a!wa/ necea"/ that cente" o +a an$ cente" o 0"a#it/ o a bo$/ coinci$e% E&'!ain. Ans. @o, centre of mass and centre of gravity may not coincide. &he centre of mass and centre of gravity coincide with each other in uniform gravitational field, such as near the earth!s surface but if the gravitational field is not uniform then the centre of mass and centre of gravity of the body do not coincide. /Alternative' centre of mass and centre of gravity coincide for ordinary bodies, but the centre of mass and centre of gravity of the body do not coincide if the body has so large dimension2
6. i#e the $i+eniona! o"+*!a o" the 'otentia! $ie"ence an$ the 'eciic heat ca'acit/. Ans. Ootential (ifference' Ootential difference + work done charge (im of p.d. + dim of work done dim of charge
+ 3$5&963$4 54 &46 + 3$5&96 pecific heat capacity' (im of sp. Heat capacity +
dimension of heat energy dimensionof mass x dimensionof temperature
+ 3$5&963$6 + 35&96 / you can write in terms of temperature/P2 and in terms of charge/E22
<. Two o"ce ha#e e7*a! +a0nit*$e an$ thei" "e*!tant a!o ha the a+e +a0nit*$e. in$ the an0!e between o"ce.
Ans. 5et, A and : be two vectors such that A + x, E + x and their resultant - + x. From parallelogram law of vectors - + A ; : ; A:cos= 8r, x + x ;x ;xcos= 8r, 7 + ; cos= 8r, cos= + 97 + 74
1. Since the +oon i contant!/ att"acte$ towa"$ the ea"th b/ the 0"a#itationa! att"actionwh/ $oe not it c"ah into the ea"th%
Ans. &hough moon is continuously attracted towards the centre of earth, but it does not fall on to the earth. It is because the gravitational attraction of earth provides necessary centripetal force to the moon for its orbital motion around the earth.
. S*''oe the "a$i* o the ea"th i to h"in, b/ F- it +a "e+ainin0 the a+e- wo*!$ the acce!e"ation $*e to 0"a#it/ 0 inc"eae o" $ec"eae an$ b/ what 'e"cent%
Ans. &he acceleration due to gravity is given by, g + *$- QQQQ./i2 #hen radius is shrink by R, -! + - 1 R of - +4.?B- g! + *$/4.?B-2
+ *$4.?S4>- + 7.4> *$- + 7.4>g &herefore, acceleration due to gravity increases. increase in g + 7.4>g 1 g + 4.4>g
increase ∈ g x 744R g
Oercentage increase in g +
+
0.04 g
g
x 744R
+ >R
. An at"ona*t "e!eae a 'oon o*t o a ate!!ite in the 'ace. Wi!! the 'oon a!! on the ea"th% Ans. (ue to inertia, the speed of the spoon is e%ual to the speed of the satellite. &he orbit of the satellite is independent of the mass of the satellite, so, the spoon continuous to follow the motion of the satellite. Hence, the spoon does not fall on the earth surface.
. Can th"ee #ecto" !/in0 in a '!ane 0i#e ?e"o "e*!tant% E&'!ain. Ans. &he resultant of three vectors not in the same plane cannot give a Cero resultant. &he resultant of two vectors in a plane cannot balance the third vector in the different plane.
2. I hea#ie" bo$ie a"e att"acte$ +o"e t"on0!/ b/ the ea"th- wh/ $o the/ not a!! ate" than !i0hte" one%
Ans. Ans. &he acceleration due to gravity of a body is, g+ *$ - It shows that acceleration due to gravity is independent of mass of the body. &herefore, all masses fall with the same rapidity provided air resistance is neglected.
3. S*''oe /o* chooe o"ce ()- !en0th () an$ ti+e (T) to be the *n$a+enta! *nit. How wo*!$ /o* e&'"e the *ni#e"a! 0"a#itationa! contant () $i+eniona!!/ in te"+ o - an$ T%
Ans. &he gravitational force is given by,
F + *m7md 8r, * + Fdm7m 8r, * + Fd/Fa2 8r, * + a dF @ow, dimensional formula of gravitational constant is, ¿
3*6 +
dimensional formulaof a X dimensional formula of d ¿ ¿
+ 3$4 5 &963$4 5 &463$5&96 + 3$97 5< &96
4. I the 0!oba! wa"+in0 contin*e. Ice nea" the 'o!e wi!! +e!t an$ be a$$e$ to the ocean. What eect wi!! thi ha#e on the !en0th o the $a/%
Ans. If the polar ice melts, the water /from melted ice2 will spread over the surface of the earth. (ue to this reason, the moment of inertia will increase and angular velocity /02 will decrease. ince, time period, &+ G0, the time period increases. Hence, the length day will increase.
5. The *n '*!! on the +oon with a o"ce that i +o"e than twice the +a0nit*$e o the ea"th att"act the +oon. Wh/ then $oe not the *n ta,e the +oon awa/ "o+ the ea"th%
Ans. &he moon is continuously revolving around the earth. &he gravitational force of attraction of earth provides necessary centripetal force to the moon for its orbital motion around the earth. o, the sun does not take the moon away from the earth though the sun pulls on the moon with a force that is more than twice the magnitude of the earth.
ON QUESTIONS 7. tate triangle law of vector addition. 8btain an expression for the resultant of two vectors O and E inclined at =. . #hat is conical pendulumT how that the period of oscillation of this pendulum is given by, & + G
√
Lcos θ g
where symbols have their usual meanings.
<. (efine moment of inertia and angular momentum. Mstablish a relation between them. >. #hat is escape velocityT (erive its expression on the surface of the earth. U. #hat do you understand by gravitational potential energy in the earth!s gravitational fieldT (erive its expression for any point around the earth!s surface. S. #hat is second pendulumT how that the motion of the bob of a pendulum is simple harmonic and hence obtain an expression for its time period.
V. (efine centripetal acceleration and obtain an expression for it in a uniform circular motion of length l. B. #hat do you mean by moment of inertia obtain an expression for the moment of inertia of a thin and uniform rod about an axis passing through one end and perpendicular to its length. ?. #hat is centripetal forceT Find its expression. 74. (erive the expression for the orbital velocity, time period, and height of artificial satellite from the surface of the earth. 77. (efine tor%ue and couple in rotational motion. (erive the expression of work done by couple. 7. (erive the expression for the variation of acceleration due to gravity due to the rotation of the earth. 7<. (erive the expression for the acceleration for a cylinder rolling down on inclined plane in terms of angle of inclination = with horiContal, radius of cylinder r and radius of gyration P. 7>. how that the small oscillations of a mass loaded spring suspended vertically are simple harmonic. Also deduce its time period. 7U. (erive an expression for the gravitational potential at a point due to mass $. 7S. #hat is H$T how that the motion of a bob of a simple pendulum id simple harmonic. Find its time period. 7V. tate and explain parallelogram law of vector. 7B. #hat is geostationary satelliteT 8btain an expression for the total energy of a satellite orbiting round the earth.
@W$M-I)A5 O-8:5M$ 7. An electric fan is turned off, and its angular velocity decreases uniformly from U44 revmin to 44 revmin in > sec, find /a2 angular acceleration and the number of revolutions made by the motor in > sec interval /b2 how many more seconds are re%uired for the fan to come to rest if the angular acceleration remains constantT /Ans. V.BUradsec , <.<, .SS sec2 . )alculate the period of oscillation of a simple pendulum of length 7.Bm with a distance of 4 cm and released. #hat will be the values of /i2 the P. M. and /ii2the velocity of the bob at the lowest point of the swingT / Ans. 4.>X, 4.>Vms2 <. A simple pendulum has a period of >.second, when the pendulum is shortened by 7m the period is <.V second. From these measurements, calculate the acceleration of free fall and the original length of the pendulum. /Ans. 74ms , >.Um2 >. An earth satellite moves in circular orbit with an orbital speed of S44 ms. Find /i2 the time of revolution /ii2 the centripetal acceleration of the satellite in its orbit. /Ans. 7VU min, <.V ms 2 U. A constant tor%ue of 44 @m turns a wheel about its centre. &he $. I. about this axis is 744 kgm . Find the angular velocity gained in > s and the P. M. gained after 4 revolutions. / Ans. .>rads , U7< kg. V. An ob"ect is undergoing simple harmonic motion with a period of G and amplitude A + 4.> m at t + 4 the ob"ect is at x + 4. How far is the ob"ect from the e%uilibrium position when t + G74. / Ans. B.VV x 74 9<2
B. A small body of mass 4.7 Pg is undergoing H$ of amplitude 7 m and period 4. sec. /a2 #hat is the maximum value of force acting on itT /b2 if the oscillation is produced by a spring, what is the constant of the springT/ Ans. ?B.U?@, ?B.SU @m2 ?. An ob"ect of mass 4.U Pg is rotated in a horiContal circle by a string 7 m long. &he maximum tension in the string before it breaks is U4 @. #hat is the greatest number of revolutions per second of the ob"ectT /Ans. 7.U?2 74. At what angle should the road be banked so that a car running at >4 kmhr may be safely able to go round a circular turn of 44 m radiusT &ake g + ?.Bmsec . / Ans. <.U kgm , how long does it take to come to restT /Ans. S.> rev, B sec2 7. A ballet dancer spins about a vertical axis at 7 rev per second with arms outstretched. #ith her arms folded, her $I about the same axis decreases to >4R of the initial $I. )alculate her new rate of revolution and her final angular velocity. 7<. A ballet dancer spins with .> revs with her arms outstretched when the moment of inertia about the axis of rotation is 7. #ith her arms folded, the moment of inertia about the same axis becomes 4.S I. )alculate the new rate of spin. 7>. &he mass of the earth is S x 74 > and that of the moon is V.> x 74 kg. if the distance between their centers is <.B x 74 B m, calculate at what point on the line "oining their centers there is no gravitational force. 15. A particle executing H$ with a fre%uency of 7G has a peak amplitude of 7. cm of either side of the e%uilibrium position. (etermine its velocity and acceleration at a displacement of 4.Scm.
