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451.

A spring is cut into two equal halves. How is the spring constant of each half affected?

Answer» Spring constant of each half becomes twice the spring constant of the original spring.
452.

If the momentum of a body is increased by 100%, then the percentage increase in the kinetic energy isA) 150%B) 200%C) 225%D) 300%

Answer»

D) 300%

Explanations:

p = 100% x p + p

 =2p

K'=(p')2/2m

 =4p2/2m

4K=3K +K

=300% K + K

= 300% K+K

KE becomes four times. It means that the kinetic energy increase by 300%.

453.

A spring is cut into equal halves.How is spring constant of each half affected?

Answer»

We know that F α l

i.e. F = k l

∴ For a given force, k α \(\frac {1}{l}\) since extension a length. If length is halved then the spring constant doubles.

454.

A light body and a heavy body have same momentum. Which one will have greater kinetic energy?

Answer»

We know that KE = \(\frac{p^2}{2m,}\)

given p is same 

∴ k E α \(\frac{1}{2m}\)

∴ Lighter body will have greater kinetic energy.

455.

Two equal masses m1 and m2 are moving along the same straight line with velocities 5 ms-1 and -9 ms-1 respectively. If the collision is elastic, then calculate the velocities after the collision of m1 and m2, respectively(a) -4 ms-1 and 10 ms-1 (b) 10 ms-1 and 0 ms-1 (c) -9 ms-1 and 5 ms-1 (d) 5 ms-1 and 1 ms-1

Answer»

(c) -9 ms-1 and 5 ms-1

456.

A light body and a heavy body have same linear momentum. Which one has greater K.E.?

Answer»

Here, pi = pz , m1v1 = m2v2

∴ \(\frac{v_2}{v_1}=\frac{m_1}{m_2}..........(i)\)

As \(E_2=\frac{1}{2}m_2v^2_2\)

and \(E_1=\frac{1}{2}m_1v^2_1\)

∴ \(\frac{E_2}{E_1}=\frac{\frac{1}{2}m_2v^2_2}{\frac{1}{2}m_1v^2_1}\)

\(=\frac{m_2}{m_1}(\frac{v_2}{v_1})^2\)

using (i) \(\frac{E_2}{E_1}=\frac{m_2}{m_1}\times(\frac{m_1}{m_2})^2\)

If m1 < m2, E2 < E1

or E1 > E2

i. e., lighter body has more K.E.

457.

If the momentum of a body is increased by 100%, then the percentage increase  in the kinetic energy is A) 150%B) 200%C) 225%D) 300%

Answer»

D) 300%

Explanations:

p'=100% x p+p

=2p

K'=(p')/2m

=4p/2m

4K= 3K + K

=300% K + K

KE becomes four times. It means that the kinetic energy increases by 300%.

458.

Give explanations for the following Why a number of Bombay films were about the lives of migrants.

Answer»

Bombay became an attractive destination for people seeking jobs after the British administration replaced Surat with Bombay as its principal western port. The consequent increase in trade and industries led to a great influx of people. Thus, migrants were (and still are) an important facet of Bombay. Most of the people in the film industry were migrants themselves, and wanted to portray the plight of this class of people through films. Thus, a number of Bombay films were about the lives of migrants.

459.

Give explanations for the following What led to the major expansion of Bombay’s population in the mid-nineteenth century?

Answer»

In mid-seventeenth century, Bombay became East India Company’s principal western port, replacing Surat. Later, by the end of the nineteenth century, it had become an important administrative as well as industrial centre. All through these years, the prospects for trade and commerce, and employment kept increasing, thereby making Bombay an attractive destination for migrants.

460.

A standard car developes 40 H.P. Find the maximum speed the car can attain agains a resistance of 20kg wt. due to air and friction. Gvien efficiency of the engin is `25%.1H.P.=746W ` and `g=10ms^(-2)`.

Answer» Here,
`P=40 H.P. =40xx746wat t`
`v=?F=20kg wt. =20xx10N`
`eta =25%, g=10m//s^(2)`
As ` eta=("output power")/("input power")`
`:.` output power = force `xx` velocity
`:. "velocity" =("output power")/("force")`
`v=(7460)/(20xx10)=37.3m//s`
461.

Force acting on a particle moving along x-axis as shown in figure. Find points of stable and unstable equlibrium. .

Answer» Correct Answer - A::B::C::D
At `A,x=0` and `F=0`
For `xgt0, F= + ve` i.e. force is in the direction of displacement. Hence A is unstable equilibrium position.
same concept can be applied with E also.
At point `C,F =0`
for`xgtx_C , F = -ve`
Displacement is positive and force is negative (in oppsite direction of displacement). therefore, C point is stable equilibrium point.
462.

The force acting on a body moving along x-axis varitian of the particle particle shown in the figure. The body is in stable equlilbrium at .A. `x=x_(1)`B. `x=x_(2)`C. both `x_(1)` and `x_(2)`D. neither `x_(1)` nor `x_(2)`

Answer» Correct Answer - B
`F=0 at x=x^(2)`. When displaced from `x_(2)` in negative direction, force is positive i.e. in the opposite direction of displacement. displacement. Similarly, when displaced in positive dirction, force is negative.
463.

The force acting on a body moving along x-axis varitian of the particle particle shown in the figure. The body is in stable equlilbrium at .A. `x=x_(1)`B. `x=x_(2)`C. Both `x_(1)` and `x_(2)`D. Neither `x_(1)` nor `x_(2)`

Answer» Correct Answer - B
(b) When displaced from `x_(2)` in negative direction, force is positive. So, this force is restoring in nature and will bring the body back. Hence, at `x_(2)` body is in stable equilibrium position.
464.

A spark is produced when two stones strike against each other. Why?

Answer» Work done in striking the two stones against each other is converted into heat. This apppears as a spark.
465.

Assertion: Energy associated with a mere kilogram of matter is `9 xx 10^16 J` Reason: It follows from the relation `E = mc^2`.A. If both assertion and reason are true and reason is the correct explanation of assertion.B. If both assertion and reason are true not but reason is not the correct explanation of assertion.C. If assertion is true but reason is falseD. If both assertion and reason are false.

Answer» Correct Answer - A
Energy associated with 1 kg of matter,
`E= mc^2 = 1 xx (3 xx 10^8)^2 J=9 xx 10^(16) J`
466.

How much mass is converted into tenergy per day in a nuclear power plant operated at `10^(7)` kW?A. 9.6 gB. 9.63 kgC. 8.6 gD. 7 g

Answer» Correct Answer - A
(a) `P= 10^(7) kW =10^(10) W=10^(10)Js^(-1)`
Time,t=1 day `=24xx60xx60 s`
Energy produced per day
`E=Pt=10^(10)xx24xx60xx60=864xx10^(-3)kg=9.6 g`
As `E=mc^(2)`
`:.m=(E )/(c^(2))=(864xx10^(12)J)/((3xx10^(8))^(2)ms^(-1))=9.6xx10^(-3) kg=9.6 g`
467.

Assertion : When current is drawn from a cell, chemical energy is converted into heat energy. Reason : This is because wire through which current flows gets heated.A. If both, Assertion and Reason are true and Reason is correct explantion of Assertion.B. If both, Assertion and Reason are true but Reason is not a correct explanation of the Assertion.C. If Assertion is true but the Reason is false.D. If both, Assertion and Reason are false.

Answer» Correct Answer - D
When a cell supplies current, chemical energy of cell is converted into electrical energy. Conversion to heat is partial. Choice `(d)` is correct.
468.

One milligram of matter is converted into energy. The energy released will beA. `9xx10^6` JB. `9xx10^8` JC. `9xx10^10` JD. `9xx10^12` J

Answer» Correct Answer - C
Here, m = 1 mg = `1 xx 10^(-3) g = 1 xx 10^(-6)` kg
According to Einstein mass-energy equivalence
`E = mc^2`
where c is the speed of light in vacuum
`therefore` `E=(1xx 10^(-6) kg)(3 xx 10^8 m s^(-1))=9 xx 10^(10)J`
469.

If a body of mass 200 g falls a height 200 m and its total P.E. is converted into K.E. at the point of contact of the body with earth surface. Then what is the decrease in P.E. of the body at the contact. `(g=10m//s^(2))`A. 900 JB. 600 JC. 400 JD. 200 J

Answer» Correct Answer - C
(c ) Mass of the body, m=200 g`=200xx10^(-3)`kg
Height of body, h=200 m
Potential energy, U=mgh`=200xx10^(-3)xx10xx200=400 J`
Therefore, Decrease in potential energy at the surface =400 J.
470.

In an exothermic chemical reaction, is mass being converted into energy?

Answer» Yes, mass is converted into heat energy, though this mass is too little.
471.

To what extent does government regulation and new laws solve problems of pollution? Discuss one example each of the success and failure of legislation to change the quality of(a) public life(b) private life

Answer»

Government laws play an important role in controlling the rates of pollution in a city. However, simply passing laws is not enough. They need to be properly enforced as well. It is also a fact that people tend to find ways of getting around laws. So, apart from legislations, government also needs to carry out intensive public awareness programmes aimed at educating the public about the need and ways of controlling pollution; and about how they too have a stake in environmental governance. Example to show the success of legislation to change the quality of

Public life - The Bengal Smoke Nuisance Commission, established as per the Bengal Smoke Nuisance Act of 1905, was successful in controlling industrial smoke in colonial Calcutta.

Private life - The British government passed the Clean Air Act in 1956. This law was aimed at controlling domestic sources of smoke pollution, and to do so, it introduced the concept of smokeless zones. In these areas, smokeless fuels had to be burnt. As a result, air pollution in British cities was substantially reduced. Example to show the failure of legislation to change the quality of Public life - By the 1840s, British cities such as Derby, Leeds and Manchester had smoke control laws in place. However, these laws did not succeed much in controlling smoke emission. Since smoke is not easy to monitor or measure, it was easy for factory and steam engine owners to get away with small adjustments to their machinery, and this did nothing to stop smoke.


Private life - During the colonial period, a huge population depended on dung and wood as fuel in their daily life. This was an important source of air pollution in Calcutta. Though successful in controlling industrial smoke, the Bengal Smoke Nuisance Commission found it difficult to control this domestic smoke.

[Note: The following can also be a possible answer to the second part of this question.]
Example to show the success of legislation to change the quality of

Public life - The British state used public funds to provide for entertainment forms such as museums, art galleries and libraries for the working classes.

Private life - British administrative officials built houses in new suburbs for fulfilling the housing needs of the working classes. Example to show the failure of legislation to change the quality of

Public life - The Underground railway enhanced transport, but caused the demolition of many houses, rendering their inhabitants homeless.

Private life - The availability of one-room tenements and no housing facilities for a major part of the industrial revolution time period caused the family to get divided into smaller units. There were even cases where rural people had to leave their families behind and live alone in the urban areas where they worked.

472.

How did people entertain themselves in the chawls of Bombay? 

Answer»

The people in the chawls of Bombay entertained themselves in the following ways. 

  • Streets were used for different leisure activities. Magicians, monkey players or acrobats performed their acts here.
  • People used to exchange news about jobs, strikes, riots or demonstrations. 
  • Liquor shops and akharas too came up where people spent their time.
473.

Explain the factors which led to the expansion of Bombay.

Answer»

(i) Bombay as capital city : Bombay became the capital of the Bombay Presidency in 1519. after the Maratha defeat in the Anglo – Maratha war. The city quickly expanded. With the growth of trade in cotton and opium, large communities of traders and bankers as well as artisans and shopkeepers came to settle in Bombay. 

(ii) Industrialisation: The establishment of textile mills led to a fresh surge in migration. The first cotton textile mill in Bombay was established in 1854. By 1921, there were So cotton mills with about 1,46,000 workers. Only about one-fourth of Bombay’s inhabitants between 1881 and 1931 were born in Bombay ,the rest came from outside. Large numbers flowed in from the nearby district of Ratnagiri to work in the Bombay mills. 

(iii) Introduction of railways: The first railway was introduced from Bombay to Thane in 1853 It was at the junction head of two major railways. The development of railway encouraged an even higher scale of migration into the city. 

(iv) Famines: Famines in the dry regions of Kutch drove large number of people into Bombay in 1888-89. The flood of migrants in some years created panic and alarm in official circles. 

(v) Bombay as a film city: By 1925. Bombay had become India’s film capital. Most of the people in the film industry were themselves migrants who came from cities like Lahore. Calcutta. Madras, etc

474.

Explain any three features of chawls of Bombay (Mumbai).

Answer»

The following were the three features of chawls of Bombay. 

  • Chawls were multi-storeyed structures that had been built from at least the 1860s in the native parts of the town. 
  • Each chawl was divided into smaller one-room tenements, which had no private toilets.
  • Chawls were also the place for the exchange of news about jobs, strikes, riots or demonstrations.
475.

State any three characteristics of the ancient cities. 

Answer»

The following were the three characteristics of the ancient cities. 

  • Towns and cities, that first appeared along river valleys, such as Ur, Nippur and Mohenjodaro in ancient times, were larger in scale than other human settlements of those times. 
  • There were certain conditions needed for the development of ancient cities. It could develop only when an increase in food supplies made it possible to support a wide range of non-food producers.
  • Cites were often the nucleus of political power, administrative network, trade and industry, religious institutions, and knowledge production. It supported variegated social groups such as artisans, merchants and priests.
476.

IF a lighter body (mass `M_(1)` and velocity `V_(1)`) and a heavier body respective kinetic energies `E_(1)` and `E_(2)` are in the ratioA. `M_(2)V_(2) lt M_(1) V_(1)`B. `M_(2)V_(2) =M_(1)V_(1)`C. `M_(2)V_(1) =M_(1)V_(2)`D. `M_(2)V_(2) gt M_(1)V_(1)`

Answer» Correct Answer - D
477.

Two bodies of masses m and 2m have same momentum. Their respective kinetic energies `E_(1 )` and `E_(2)` are in the ratioA. `1:2`B. `2:1`C. `1:sqrt(2)`D. `1:4`

Answer» Correct Answer - B
478.

An ice cube has been given a push and slides without friction on a level table . Which is correct?A. It is stable equilibrium.B. It is unstable equilibrium.C. It is natureal equilibrium.D. It is not in equilibrium.

Answer» Correct Answer - C
The act cube is in neutral equilibrium .Its zero acceleration is avidence for equilibrium .
479.

A stationary particle explodes into two particles of masses x and y, which move in opposite directions wit h velocity `v_(1)and v_(2).` The ratio of their kinetic energies `(E_(1):E_(2))` isA. 1B. `(xv_(2))/(yv_(1))`C. `x/y`D. `y/x`

Answer» Correct Answer - D
480.

A stone tied to a string of length `L` is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time the stone is at lowest position and has a speed `u` . Find the magnitude of the change in its velocity as it reaches a position, where the string is horizontal.A. `sqrt((u^(2)-2gl))`B. `sqrt(2gl)`C. `sqrt((u^(2)-gl))`D. `sqrt((2u^(2)-gl))`

Answer» Correct Answer - D
481.

A stone of mass 0.2 kg is tied to one end of a string of length 80 cm. Holding the other and, the stone is whiled into a vertical circle. The minimum speed of the stone and tension at the lowest point of circular path so that it just comletes the circle areA. `5ms^(-1),10N`B. `6.32ms^(-1),12N`C. `6.32ms^(-1),10N`D. `2ms^(-1),10N`

Answer» Correct Answer - B
482.

A particle of mass 200 g is moving in a circle of radius 2 m. The particle is just looping the loop. The speed of the particle and the tension in the string at highest point of the circule path are `(g=10ms^(-2))`A. `4 ms^(-1),5N`B. `4.47ms^(-1),` zeroC. `2.47ms^(-1),` zeroD. `1 ms^(-1),` zero

Answer» Correct Answer - B
483.

A stone is dropped by an astronaut from a height of 1.47 m above the surface of a planet. When stone reaches a point P at a height of 0.32 m it attains a speed of `4.1 m//s` Is the planet earth ?

Answer» Correct Answer - [No]
484.

Figure shows four situations in which a force is applied to a block. In all four cases, the force has the same magnitude, and the displacement of the block is to the right and of the same magnitude. Which of the following cases work done by the applied force on the block zero? A. (i)B. (ii)C. (iii)D. (iv)

Answer» Correct Answer - A
Work done by the applied force is zero in (i) because in case (i) both the force and displacement are mutually perpendicular.
485.

A ball of mass 100 gm is projected upwards with velocity `(10 m//s)`. It returns back with `(6 m//s)`. Find work done by air resistance .

Answer» Correct Answer - B::C
From work energy thergy theorem,
`W_("net") =W_("mg") + W_("air") =1/2m(v_(f)^(2)-v_(i)^(2))`
`rArr 0 + W_(air) =1/2xx0.1[(6)^(2)-(10)^(2)]=-3.2J`
486.

A block of 1 kg is kept on a rough surface of an elevator moving up with constant velocity of 5 m/s. In 10 second work done by normal reaction (no sliding on incline surface) (i) from ground frame is 320 J (ii) is equal to work done by friction force in elevator frame (iii) is equal to work done by friction in ground frameA. (i)B. (ii), (iii)C. (i), (ii)D. only (iii).

Answer» Correct Answer - C
487.

Work is said to be done by a force acting on a body, provided the body is displaced actually in any direction except in a direction perpendicular to the direction of the force. Mathematically, `W=vec(F). vec(c)=Fs cos theta`, Whereas energy is capacity of a body to do the work, power is the rate at which the body can do the work. `P=(W)/(t)=vec(F).(vec(s))/(t)=vec(F). vec(upsilon)` Both, work and energy are measured in joule and power is measured in watt. With the help of the comprehension given above, choose the most appropriate alternative for each of the following question `:` A box is pushed through `4.0 m` across a floor offering `100N` resistance. Work done by the applied force isA. `400J`B. `-400 J`C. `25 J`D. `0.04 J`

Answer» Correct Answer - A
`W=F s cos theta = 100 xx 4 cos 0^(@)=400J`
488.

A particle moves along x-axis from `x=0` to `x=2` m under the influence of a force F (in N) given by `F=3x^(2)+2x-5.` Calculate the work done

Answer» `W=underset(0)overset(2)int(3x^(2)+2x-5)dx`
`W= underset(0)overset(2)int(3x^(2)+2x-5)dx`
`=3|(x^(3))/(3)|_(0)^(2)+2|(x^(2))/(2)|_(0)^(2)-5|x|_(0)^(2)`
`=8+4-10=2J`
489.

Work is said to be done by a force acting on a body, provided the body is displaced actually in any direction except in a direction perpendicular to the direction of the force. Mathematically, `W=vec(F). vec(c)=Fs cos theta`, Whereas energy is capacity of a body to do the work, power is the rate at which the body can do the work. `P=(W)/(t)=vec(F).(vec(s))/(t)=vec(F). vec(upsilon)` Both, work and energy are measured in joule and power is measured in watt. With the help of the comprehension given above, choose the most appropriate alternative for each of the following question `:` A truck draw a tractor of mass `1000 kg ` at a steady rate of `20 ms ^(-1)` on a level road. The tension in the coupling is `2000N`. Power spent on the tractor isA. `40 W`B. `20 W`C. ` 20 kW`D. `40 kW`

Answer» Correct Answer - D
Force applied `=` tension is coupling `=2000N`
As `P=Fupsiloncos theta`
`:. P= 2000 xx 20 cos 0^(@)= 40000 W = 40 k W `
490.

A particle is displaced from `x=-6` m to `x=+6` m A force F acting on the particle during its motion is shown in figure -3.102 Graph between work done by this force (W) and displacement (x) should be A. B. C. D.

Answer» Correct Answer - A
491.

Velocity-time graph of a particle of mass (2 kg) moving in a straight line is as shown in Fig. 9.20. Find the word done by all the forces acting on the particle. .A. 400 JB. `-400` JC. `-200` JD. 200 J

Answer» Correct Answer - B
492.

A body with mass `2kg` moves in one direction in the presence of a force which is described by the potential energy graph. If the body is released from rest at `x=2m`, then its speed when it crosses `x=5m` is `:-` A. ZeroB. 1 `ms^(-1)`C. `2 ms^(-1)`D. `3 ms^(-1)`

Answer» Correct Answer - C
493.

A block of mass `m=2kg ` is pulled by a force `F=40 N` upwards through a height `h=2 m.` Find the work done on the block by the applied force `F` and its weight mg. `(g=10m//s^2)`.

Answer» Weight of the block, `mg=(2)(10)=20N`
Work done by the applied force,
`W_(F) = Fs cos theta = Fh cos 0^(@)` (Here,s=h=2m and angle between force and displacement is `0^(@))`
or ` W_(F)=(40)(2)(1)=80 J` Similarly, work done by its weight ,
`W_(mg)=(mg)(h) cos180^(@)`
or `W_(mg)=(20)(2)(-1)=-40 J`
494.

The velocity-time graph of a particle moving in a straight line is shown in figure. The mass of the particle is `2kg`. Work done by all the forces acting on the particle in time interval between `t=0` to `t=10s` is A. 300 JB. `-300` JC. 400 JD. `-400` J

Answer» Correct Answer - A
495.

A plank of mass 10 kg and a block of mass 2 kg are placed on a horizontal plane as shown in the figure. There is no friction between plane and plank. The coefficient of friction between block and plank is 0.5 .A force of 60 N is applied on plank horizontally. In first 2 s the work done by friction on the block is A. `-100 J`B. 100 JC. zeroD. 200 J

Answer» Correct Answer - B
(b) Maximum acceleration of 2 kg block due to friction can be `mu g or 5 ms^(-2)`.
Combined acceleration, if both move together with same acceleration would be,
`a=(60)/(12)=5ms^(-2)`
Since, both accelerations are equal, upper block will move with acceleration `5ms^(-2)` due to friction.
In first two seconds, `s=(1)/(2)at^(2)=(1)/(2)xx5xx4=10m`
and force of friction, f=ma=10 N
`:. " " W_(f)=fs cos0^(@)=100J`
496.

These questions consists of two statements each printed as Assertion and Reason. While answering these question you are required to choose any one of the following five reponses (a) If both Assertion and Reason arecorrect and Reason is the correct explanation of Asserrtion. (b) If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion. (c ) If Assertion is true but Reason is false. (d) If Assertion is false but Reason is true. Assertion The work done in bringing a body down from the top to the base along a frictionless inclined plane is the same as the work done in bringing it down from the vertical side. Reason The gravitational force on the body along the inclined plane is the same as that along the vertical side.

Answer» Correct Answer - B
(b) Change in potential energy is same.
497.

Asseration : A body is moved from `x=2` to `x=1` under a force `F =4x, the work done by this force is negative. Reason : Force and displacement are in opposite directions .A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.B. If both Assertion and Reason are true and the Reason is not the correct explanation of the Assertion.C. If Assertion is true, but the Reason is falseD. If Assertion is false but the Reason is true.

Answer» Correct Answer - A
498.

Asseration : Corresponding to displacement-time graph of a particle moving in a the body is positive. Reason : Speed of particle is increasing.A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.B. If both Assertion and Reason are true and the Reason is not the correct explanation of the Assertion.C. If Assertion is true, but the Reason is falseD. If Assertion is false but the Reason is true.

Answer» Correct Answer - A
Slope of `S-t` graph is increasing.
Therefore, speed of the particle is increasing.
499.

If kinetic energy of a body is increasing then.A. work done by conservative forces must be positive.B. work done by conservative forces may be positive.C. work done by conservative forces may be zeroD. work done by non-conservative forces may be zero

Answer» Correct Answer - B::C::D
500.

Nuclear fission and fusion reaction are the examples of conversion of mass into energy. Can we say that “strictly speaking, mass converted into energy even in the exothermic chemical reaction”?

Answer»

Yes, mass is converted into mass energy in an exothermic chemical reaction also.

But the mass change in a chemical reaction is about a million times less than in a nuclear reaction.