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12051.

Two blocks A and B of mass m and 2m respectively are connected by a spring of force constant k. The masses are moving to the right with uniform velocity v each, the heavier mass, leading the lighter one. The spring is of natural length in the motion. Block B collides head on with a third block C of mass m, at rest, the collision being completely inelastic. Determine the velocity of blocks at the instant of maximum compression of the spring.

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ANSWER :`3v//4`
12052.

If vecr_(1)andvecr_(2) are position vectors, then the displacement vector is

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`vecr_(1)xxvecr_(2)`
`vecr_(1).vecr_(2)`
`vecr_(1)-vecr_(2)`
`vecr_(2)+vecr_(1)`

ANSWER :A::B::C
12053.

Wavelength length of light in denser medium is 4000A^@ it is grazing into a rarer medium. If critical angle for the pair of media is Sin^-1(2/3) then the wave length of light in rarer medium is

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`4000A^@`
`2666A^@`
`8000A^@`
`6000A^@`

ANSWER :D
12054.

Define projectile. Give two examples.

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SOLUTION :When an object is thrown in the air with some initial velocity (NOT just upwards), and then allowed to move under the action of GRAVITY alone, the object is KNOWN as a projectile.
Example :
1. An object dropped from window of a moving train.
2. A bullet fired from a rifle.
12055.

A cone of radius .R. and height H is immersed fully inside a liquid of density by means of a string. The force due to the liquid acting on the slant surface of the cone is (neglect atmospheric c pressure)

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`rho pi g HR^(2)`
` pi g HR^(2)`
`(4)/(3) pi rhog HR^(2)`
`(2)/(3) pirho GHR^(2)`

ANSWER :D
12056.

When two soap bubbles of radii r_1 and r_2 (r_2>r_1)coalese, the radius of curvature of common surface is

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`(r_2 - r_1)`
`(r_2 + r_1)`
`(r_2-r_1)/r_1r_2`
`(r_1r_2)/(r_1 - r_2)`

ANSWER :D
12057.

find the amplitude of vibration.

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`sqrt(((mv^(2))/(k)))`
`sqrt(((mv^(2))/(2k)))`
`sqrt(((mv^(2))/(4K)))`
None of these

Solution :Here, `OMEGA=sqrt(((k)/(2m)))`
`therefore""E_(0)=(1)/(2)(2m)A^(2)omega^(2)`
or `(mv^(2))/(4)=mA^(2)omega^(2)or (mv^(2))/(4)=mA^(2)(k)/(2m)`
`therefore""A=sqrt(((mv^(2))/(2k)))`
12058.

The time period of a seconds pendulum is measured repeatedly for three time by two stop watches A, B. If the readings are as follows {:("S.NO",A,B),(1,2.01 sec,2.56 sec),(2,2.10sec,2.55sec),(3,1.98 sec,2.57sec):}

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A is more ACCURATE but B is more precise
B is more accurate but A is more precise
A,B are EQUALLY precise
A,B are equally accurate

Answer :A
12059.

Three masses 3 kg 4 kg and 5 kg are located at the comers of an equilateral triangle of side 1 m. Locate the centre of mass of the system.

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SOLUTION :`(X,y) -(0.54 m, 0.36 m)`
12060.

The time period of a particle performing linear SHM is 12s. What is the time taken by it to cover a distance equal to half its amplitude starting its motion from the mean position?

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1 SEC 
2 sec 
3sec
4sec 

ANSWER :A
12061.

Two sound waves travel in the same direction in a medium . The amplitude of each wave is A and the phase difference between the two waves is 120^(@). The resultant amplitude will be :

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`2 A`
` 3A`
`sqrt(2)A`
A

Solution :Here `A_(1)=A,A_(2)=A, varphi=120^(@)`
The amplitude of the RESULTING WAVE is
`A_(R)=sqrt((A_(1))^(2)+(A_(2))^(2)+2A_(1)A_(2) cos varphi)`
`=sqrt(A^(2)+A^(2)+2 A A cos 120^(@))`
`= sqrt((A^(2)+A^(2)-A^(2)))=A ( :. cos120^(@)=-(1)/(2))`
12062.

A plate of area 100cm^(2) is placed on the upper surface of castor oil 2 mm thick. Taking the coefficient of viscosity to be 15.5 poise, calculate the horizontal force necessary to move the plate with a velocity of 3cms^(-1) is

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46.5 N
23.25
0.2325 N
2.325 N

Answer :C
12063.

A particle of mass 100 g is thrown verticaly upwards with the speed of 5m/s. The work done by the force of gravity during the time the particle goes up is (g=10ms^(-2))

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`-0.5J`
`-1.25J`
`1.25J`
`0.5J`

ANSWER :B
12064.

Show that -40^(@) measures the same temperature on Celsius and Fahrenheit scales.

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Solution :Let C = F= X.
`(C)/(5) = (F -32)/(9) (x)/(5) = (x- 32)/(9)` , 9x= 5x- 160
4x = - `160 RARRX = - 40^(@).`
12065.

A particle of mass m moving with velocity v collides with a stationary particle of mass 2m, makinginelastic collision. The speed of the system after collision, will be

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`(V)/(2)`
2V
`(v)/(3)`
3v

Answer :C
12066.

A terrorist ‘A’ is walking at a constant speed of 7.5 km//hr due West. At time t = 0, he was exactly South of an army camp at a distance of 1 km. At this instant a large number of army men scattered in every possible direction from their camp in search of the terrorist. Each army person walked in a straight line at a constant speed of 6 km//hr. (a) What will be the closest distance of an army person from the terrorist in this search operation? (b) At what time will the terrorist get nearest to an army person?

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ANSWER :(a) `(3)/(5) KM` (b) `8min`
12067.

A bus starts from rest with a constant acceleration of 5 ms^(-1) overtakes andpasses the bus . Find(i) at what distance will the bus overtake the car ? (ii) how fast will the bus betravelling then ?

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Answer :(ii) 1000 m (ii) `100 ms ^(-1)`
12068.

A spherical ball of mas m is kept at the highest point in the space between two fixed, concentric spheres A and B as shown in figure. The sphere A has radius R and sphere B has radius R+d. All surfaces are smooth. The diameter of ball slightly less than d. The ball is given a gentle push so thatangle made by radius vector of the ball with vertical is theta. N_(A) and N_(B) are the magnitudes of normal reaction forces on the ball exerted by spheres A and B respectively. The match the following

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ANSWER :A::B::C::D
12069.

A mass of 0.2kg is attached to the lower end of a massless spring of force-constant 200 N//m, the upper end of which is fixed to a rigid support. Which of the following statements is//are true?

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In equilibrium, the SPRING will be stretched by `1cm`.
If the mass is raised TILL the spring is unstreched state and then released, it will godown by `2cm` before moving upwards.
The frequency of oscillation will be nearly `5Hz`.
If the SYSTEM is taken to the MOON, the frequency of oscillation will be the same as on the earth.

Answer :A::B::C::D
12070.

The maximum displacement of a particle executing SHM is 1 cm and the maximum acceleration is (1.57)^(2)cm//s^(2). Its time period is……………..

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0.25s
4.0s
1.57s
3.14s

Solution :`T=2pisqrt((A)/(a_(MAX)))=2xx3.14xxsqrt((1.0)/((1.57)^(2)))=4.0s`
12071.

If Fhatk force is acting on particle has position vector (2hati-2hatj), then torque on it is …... .

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ANSWER :`F(hati-HATJ)`
`hattau=vecrxxvecF=(2hati-hatj)xxFhatk`
`:. hattau=2F(hatixxhatk)+F(hatjxxhatk)`
`=2F(-hatj)+F(hatj)=F(hati-2hatj)`
12072.

A uniform rod of length 2m and mass 5 kg is lying on a horizontal surface. The work done in raising one end of the rod with the other end in contact with the surface until the rod makes an angle 30^(@) with the horizontal is, (g=10 ms^(-2))

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25 J
50 J
`25sqrt(3)J`
`50sqrt(3)J`

ANSWER :A
12073.

A block of mass 5 kg is resting on a smooth surface. At what angle a force of 20 N be acted on the body so that it will acquired a kinetic energy of 40 J after moving 4 m?

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`30^@`
`45^@`
`60^@`
`120^@`

Solution :ACCORDING to work energy theorem
W = CHANGE in kinetic energy
`FS cos theta = 1/2 mv^2 - 1/2 m u^2`
Substituting the given values, we get
`20 XX 4 xx cos theta = 40 - 0 "" ( :. u = 0)`
or `cos theta = 40/80 = 1/2` or `theta = cos^(-1)(1/2) = 60^@` .
12074.

The radius of proton in of the order of

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`10^(15)m`
`10^(-15)m`
`10^(-14)m`
`10^(-31)m`

ANSWER :(B)
12075.

A car accelerates from rest at a constant rate alpha for sometime after which it decelerates at a constant rate beta to come to rest. If the total tiem lapsed in t seconds , find (1)the maximum velocity reached and (2)the total distance travelled.

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Solution :LET` v_(m)` be the maximum velocity and let `t_(1)` be time taken to attain it . Then using
`v=u+at` we get `v_(m)=ALPHA t_(1)`……(1)
Let `t_(2)` be the time taken by the car to stop under retardation `BETA`. Then
`0=v_(m) beta t_(2)"or"v_(m)beta t_(2)`....(2)
Eqns.(1)and(2) GIVEN
`t_(2)/t_(1)=alpha/beta"or" t_(2)/t_(1)+1-alpha/beta+1"or" t/t_(1)=(alpha+beta)/beta"or" t_(1)=beta/(alpha+beta)t`
Substituting this value of `t_(1)`in eqn.(1),
`v_(m)=(alphabeta)/(alpha+beta)t`t
Now , let `s_(1)`be the distance travelled during acceleration and let `s_(2)`be the distance travelled during retardation . Then using the equation
`v^(2)=u^(2)+2as`,we get `v_(m)^(2)=2alphas_(1)`........(3)
and `0=v_(m)^(2)-2betas_(2)`.......(4)
`:. s_(1)=v_(m)^(2)/(2alpha)=(alphabeta^(2))/(2(alpha+beta)^(2)t^(2)"and"s_(2)`
`=(alpha^(2)beta)/(2(alpha+beta))^(2)t^(2)`
`:. `Total distance `s=s_(1)+s_(2)`
`=(alphabetat^(2))/(2(alpha+beta))^(2)(alpha+beta)=(alphabetat^(2))/(2(alpha+beta))`
12076.

Moment of momentum is called angular momentum.

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ANSWER :TRUE.
12077.

A square plate of 0.1 m side moves parallel to a second plate with a velocity of 0.1 m/s, both plates being immersed in water. If the viscous force is 0.002 N and the coefficient of viscosity is 0.01 poise, distance between the plates in m is

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`0.1`
`0.05`
`0.005`
`0.0005`

ANSWER :D
12078.

A particle is at x=+5 m at t=0, x=-7m at t=6 s and x =+2 at t=10s.Find the averahe velocity of the particle during the intervals (a)t=0 to t=6s (b)t=6s to t=10s, ©t=0 to t=10 s.

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Solution :From the defination of AVERAGE velocity
`V=(trianglex)/(trianglet)=(x_(2)-x_(1))/(t_(2)-t_(1))`
(a) The average velocity between the times
t=0 to t=6s
`x_(1)=+5m, t_(1)=0, x_(2)=-7m t_(2)=6s`
HENCE `v_(1)=(x_(2)-x_(1))/(t_(2)-t_(1))=(-7-5)/(6-0)=-2ms^(-1)`
(b) The average veloctiy between the times
`t_(2)=6s" to "t_(3)=10s` is
`v_(2)=(x_(3)-x_(2))/(t_(3)-t_(2))=(2-(-7))/(10-6)=9/4 =2.25ms^(-1)`
(c) The average velocity between times `t_(1)=0" to "t_(3)=10` s is
`v_(3)=(x_(3)-x_(1))/(t_(3)-t_(1))=(2-5)/(10-0)=-0.3ms^(-1)`
12079.

Though India now has a large base in science and technology, which is fast expanding, it is still a long way from realizing its potential of becoming a world leader in science. Name some important factors, which in your view have hindered the advancement of science in India.

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SOLUTION :In my view, some important factors which have hindered the advancement of science in India are :
(i) Lack of EDUCATION, (ii) Poverty, which leads to lack of resources and lack of infrastructure, (iii) Pressure
of increasing POPULATION, (iv) Lack of scientific plannig, (V) Lack of dvelopment of work culture and self
discipline.
12080.

The escape velocity of a projectile on the surface of earth is 11.2 kms^(-1) . If a body is projected out with thrice this speed, find the speed of the body far away from the earth. Ignore the presence of other planets and sun.

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Solution :Here, `v_e = 11.2 kms^(-1) ` , velocity of projection of the BODY `v = 3v_e`. Let m be the mass of the PROJECTILE and `V_0` . be the velocity of the projectile when FAR away from the earth (i.e. out of gravitationalfield of earth). Then from the law of conservation of energy.
` 1/2 mv_0^2 = 1/2 mv^2-1/2 mv_e^2`
`v_0 = sqrt(v^2 -v_e^2) = sqrt((3v_e)^2 - v_e^2)`
` = sqrt8 XX 11.2 = 31.68 kms^(-1)`
12081.

The poisson ratio for the material of a wire is 0.4. When a force is applied on the wire, longitudinal strain is (1/100) . The perecentage change in the radius of the wire is

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0.1
0.8
0.4
0.2

Answer :C
12082.

The acceleration of a particle is given by a (t)=(3.00m//s^(2))-(2.00 m//s^(3)) t. (a) Find the initial speed V_(0) such that the particle will have the same x-coordinate at t=5.00sas it had at t=0. (b) What will be the velocity at t=5.00s?

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ANSWER :(a)` 0.833 m//s` (B)`-9.17 m//s`
12083.

Two bodies of different masses are dropped simultaneously from same height. If air friction acting on them is directly proportional to the square of their mass, then,

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lighter body REACHES the ground EARLIER
heavier body reaches the ground earlier
both reach the ground at the same TIME
Any of the aove

Answer :A
12084.

A projective has initially the same horizonal velcoity as it would acquire if it had moved from rest with uniform accleration of 3ms^(-2)for 0.5 minutes. If the maximum heightreached by it is 80m then the angle of projection is[g=10ms^(-2)]

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`TAN^(-1)(3)`
`tan^(-1)(3/2)`
`tan^(-1)(4/9)`
`sin^(-1)(4/9)`

Answer :C
12085.

A wheel rotates around a stationary axis so that rotation angle thetavaries as theta= pt^(2) where p=0.2"rad"//"sec"^(2) The total acceleration (a) of the point A at the rim at the moment t = 2.55sec. If linear velocity of the point (A) at this moment is V = 0.65m//sec is

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`0. 7 m//sec^(2)`
`0.6 m//sec^(2)`
`0.5 m//sec^(2)`
`0.4 m//sec^(2)`

ANSWER :A
12086.

Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attration. The speed of each particle is

Answer»

`SQRT((GM)/(R))`
`sqrt(2sqrt(2)(GM)/(R))`
`sqrt((GM)/(R)(1+2sqrt(2)))`
`(1)/(2)sqrt((GM)/(R)(1+2sqrt(2)))`

Answer :D
12087.

Show that for a particle in linear S.H.M., the average kinetic energy over a period of oscillation equals the average potential energy over the period.

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Solution :Consider a particle of mass m EXECUTING S.H.M. with period T . The displacement of the particle at an instant t, when time period is noted from the MEAN position is given by y`=A sin omega t`
`therefore ` VELOCITY , `V= (dy)/(dt) = A omega cos omega t`,
KINETIC energy `E_K = 1/2 mV^2 = 1/2 m A^2 omega^2 cos^2 omega t`
POTENTIAL energy `E_P =1/2ky^2 = 1/2 m omega^2 A^2 sin^2 omega t`
`(because K = m omega^2) therefore ` Average K.E. over one cycle.
`E_(k_(av)) = 1/T int_0^T E_k dt = 1/T int_0^2 1/2 mA^2 omega^2 cos^2 omega t dt`
`=1/(2T) m omega^2 A^2 int_0^T ((1+ cos 2 omegat))/2 dt = 1/(4T) m A^2 omega^2 [k+(sin 2omega t)/(2omega)]_0^T = 1/(4T) mA^2 omega^2 (T) = 1/4 mA^2 omega^2`
Average P.E. over one cycle is `E_(k_(av)) = 1/T int_0^T E_k dt = 1/T * 1/T int_0^T 1/2 mA^2 omega^2 sin^2 omega t dt`
`=1/(2T) m omega^2 A int_0^T ((1-cos 2omegat))/2 = 1/(4T) m omega^2 A^2 [1-(sin2 omega t)/(2omega)]_0^T`
`=1/(4T) m omega^2 A^2 [T] =1/4 A^2 omega^2`
From (i) and (ii) , `E_(K_(aÅ))= E_(P_(aÅ))`
12088.

In the above problem, the velocity attained by the particle in a certain interval of time will be proportional to

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m
1/m
`SQRT(m)`
`(1)/(sqrt(m))`

ANSWER :B
12089.

Equation to convert Celcius temperature in Fahrenheit is t^(@)F=5/9t^(@)C+32

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SOLUTION :`t^(@)F=9/5t^(@)C+32`
12090.

A bullet of mass m moving with velocity u passes through a wooden block of mass M = nm as shown in figure. The block is resting on a smooth horizontal floor. After passing through the block, velocity of the bullet becomes v. Its velocityrelative to the block is

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SOLUTION :Let V. be the velocity of block. Then fromconservation of LINEAR MOMENTUM.
`m u = mv+mnv^(1)(or)v^(1)=((u-v)/(n))`
`therefore` velocity of bullet relative to block will be
`v_(r) =v-v^(-1)=v-((u-v)/(n))=((1+n)v-u)/(n)`
12091.

The most elastic among the following substances is

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rubber
glass
steel
copper

Answer :C
12092.

A steel ring of radius r and cross-sectional area A is fitted onto a wooden disc of radius R (R gt r). If the Young's modulus of steel is Y, then the force with which the steel ring is expanded is ..........

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`AY (R )/(r )`
`AY [ (R-r)/(r )]`
`Y/A [ (R-r)/(r )]`
`(Yr)/(AR)`

Solution :CIRCUMFERENCE of wooden disc `=2pi R`
Circumference of steel RING `L = 2pi r `
Increase in circumference of steel ring
`l= 2pi R - 2pi r`
`= 2pi (R-r)`
STRAIN `= l/L = (2pi (R-r))/( 2pi r ) = (R-r)/(r)`
Now, Young.s modulus `Y= ("stress")/("strain") = ((F)/(A))/( (R-r)/(r))`
`therefore F = AY[ (R-r)/(r)]`
12093.

An object of mass 'm' in air experiences a drag force D=bv. The velocity of the object at any time-t assuming that it starts falling vertically under gravity from rest is (2mg)/(kb) [1-e^(-(b//m)t)]. The value of 'k' is ( acceleration due to gravity , is g).

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ANSWER :2
12094.

Consider the following statement: When jumping from some height, you should bend your knees as you come to rest, instead of keeping your legs stiff. Which of the following relations can be useful in explaining the statement Where symbols have their usual meaning

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`DeltavecP_(1)=-DeltavecP_(2)`
`DeltaE=-Delta(PE+KE)=0`
`vecFDeltat=mDeltavecv`
`DeltavecxpropDeltavecF`

ANSWER :C
12095.

Asteel wire of length 4.6 m and cross section 3 xx 10^(5)m^(2) stretches by the same amount as a copper wire of length 4.0 m and cross section 4.0 xx 10^(-5) m^(2) under the same load. Find the ratio of the Young.s modulus of steel to that of copper

Answer»

Solution :Elongation `=(Mgl)/(PIR^(2)Y)=(Mgl)/(AY)`
Since the elongations are the same in both CASES under the same load `(l_(s))/(A_(s)Y_(s))=(l_(C_(u)))/(A_(C_(u))Y_(C_(u)))`
`:.(Y_(s))/(Y_(C_(u)))((l_(s))/(l_(C_(u))))((A_(C_(u)))/(A_(S)))=(4.6)/(4.0)((4XX10^(-5))/(3xx10^(-5)))=(4.6)/(3)=(23)/(15)`
So the ratio of their MODULI of clasticity is `23:15`
12096.

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4cm and 4.8cm, respectively. The ratio of minimum and maximum velocities of fluid in this pipe is

Answer»

`(81)/(256)`
`(9)/(16)`
`(3)/(4)`
`(3)/(16)`

SOLUTION :From continuity equation, `A_(1) v_(1) = A_(2) v_(2)`
`:. (v_(1))/(v_(2)) = (A_(2))/(A_(1)) " " (A_(2))/(A_(1)) = ((pi D_(2)^(2))/(4))/((pi D_(1)^(2))/(4)) = (D_(2)^(2))/(D_(1)^(2))`
`:. (v_(1))/(v_(2)) = ((D_(2))/(D_(1)))^(2)`
`:. (v_(1))/(v_(2)) = ((4-8)/(6-4))^(2) = ((3)/(4))^(2)`
`:. (v_(1))/(v_(2)) = (9)/(16)`
12097.

The specific heat of a substance varies with temperature T as C = (AT^(2) + BT)"Cal/g-"^@C, with temperature in degree celsius. Heat is supplied by a heater of resistance 200 ohm operating at 220 volt, to heat 50 g of substance from 27^@C " to " 57^@C If the time taken is 2 hr x minute then what is he value of x ? (Given A = 2.5 xx 10^(-3) cal/gm - (""^@C)^3 and B = 12 xx 10^(-2)" cal/gm"-(""^@C)).

Answer»


ANSWER :4
12098.

In a reciprocating steam engine, the avearge pressure of steam is 50 Nm^(-2). The length of half stroke is 50 cm and area of cross section of the piston is 400 cm^(2). If the engine is making 300 strokes per minute, calculate power of the engine in k W.

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ANSWER :200kW
12099.

Why does sound travel faster in solids than in gases?

Answer»

STEEL
AIR
WATER
VACUUM

SOLUTION :steel
12100.

A particle of mass 0.5kg is executing SHM along a straight line. Its path length is 10cm and time period is 8s. Calculate its KE, PE and Te when its phase angle ispi//6 radian.

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Solution :(i) `5.923 XX 10^(-3) J, (ii) 3.949 xx 10^(-4) J , 3.856 xx 10^(-4) J`