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15651.

An open pipe is in resonance in 2^(nd) harmonic with the frequency f_(1) . Now oneend of the tube is closed and frequency is increased to f_(2) such that the resonance again occurs in n^(th) harmonic. Choose the correct option.

Answer»

`n= 3f_(2)=(5)/(4)f_(1)`
`n=5, f_(2)=(5)/(4) f_(1)`
`n=3, f_(2)=(3)/(4)f_(1)`
`n=5, f_(2)=(3)/(4)f_(1)`

Solution :In case of open PIPE, frequency of second harmonics is,
`f_(1)=(v)/(lambda)=(v)/(L) "" [ lambda=L]`
In case of closed, pipe, frequency of `n^(th)` harmonic,
`f_(2)=(mv)/(4L)` where n is odd number.
clearly `f_(2)=(n)/(4)f_(1)`
If `n=3, f_(2) LT f_(1)` which is not ACCEPTABLE
In `n=5, f_(2)=(5)/(4)f_(1)` which is acceptable
Discussion
15652.

How many unified atomic mass units are there in one kg?

Answer»

SOLUTION :`1 KG = 6.02xx10^(26)U`
Discussion
15653.

Standing sound waves are produced in a pipe that is 0.8 m long, open at one end, and closed at th other. For the fundamental and first two overtone, where along the pipe (measured from the closed end) are (a) the displacemental antinodes (b) the pressure antinodes.

Answer»


Solution :
(a) In second FIGURE, `l = (3 lambda)/(4)`
`:. (lambda)/(4) = (l)/(3) = (0.8)/(3)`
`= 0.267 m`
DISPLACEMENT ANTINODE is at
`x = (lambda)/(4) = 0.267 m`
and `x = 3(lambda)/(4) = 0.8m`
(b) Pressure antinode is displacement node: In THIRD figure,
Pressure antinode or displacement node is at
`x = 0`, `x = (lambda)/(2)`
and `x = lambda`
Discussion
15654.

Two particle of masses 1 g and 4g are moving with equal K.E. What is the ratio of their linear momentum?

Answer»

`4:1`
`sqrt2:1`
`1:2`
`1:10`

ANSWER :C
Discussion
15655.

An air pump is pumping air in to a a large vessel against a pressure of 1 atmosphere. In each stroke 1000 C. C of air enters in to the vessel. If the number of strokes made by the pump per minute is 30, the power of the pump is (1 atm = 10^(5) Pa)

Answer»

5 KW
50 KW
100 KW
50 W

ANSWER :D
Discussion
15656.

The amplitude of damped oscillator becomes 1/3 in 2s. Its amplitude after os is in times the original. The value of of n is

Answer»

`2^3`
`3^2`
`3^(1//3)`
`3^3`

ANSWER :D
Discussion
15657.

An enemy plane is flying horizontally at an altitude of 2km witha speed of 300ms^(-1). An army man with an anti-aircraft gun on the ground sights hit enemy plane when it is directly overhead and fires a shell with a muzzle speed of 600ms^(-1). At what angle with the vertical should the gun be fired so as to hit the plane ?

Answer»

<P>

Solution :LET G be the position of the gun and E that of the enemy plane flying horizontally with speed
` u = 300ms^(-1)`, when the shell is fired with a speed `v_(0)` is `v_(x) = v_(0)costheta`
Let the shell hit the plane a point P and let t be the time taken for the shell to hit plane. It is clear that the shell will hit the plane, if the horizontal distance EP travelled by the plane in time t = the distance travelled by the shell in the horizontal direction in the same time, i.e.
`uxxv = v_(x)XXT or u= v_(x) = v_(0) costheta`
` or costheta = (u)/(v_(0)) = (300)/(600)`

`=0.5 or theta = 60^(0)`.
Therefore, angle with the vertical = `90^(0)-theta=30^(0)`.
Discussion
15658.

The mass and radius of a planet are double that of earth. If the time period of a somple pendulum on the earth is T. The time period on the planet is

Answer»

T
2T
`SQRT(2)T`
`T/(sqrt(2))`

ANSWER :C
Discussion
15659.

A body of mass 6 xx 10^(24) kg (equal to mass of earth ) is to be compressed into a sphere is such a way that the escape velocity from its surface is 3 xx 10^(8) m/s. What should be the radius of the sphere in mm ____

Answer»


ANSWER :9
Discussion
15660.

A monoatomic ideal gas, initially at temperature T_1 , is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature. T_2by releasing the piston suddenly. If L_1 and L_2are the lengths of the gas column before and after expansion respectively, then T_1//T_2is given by

Answer»

`(L_1/L_2)^(2/3)`
`(L_1/L_2)`
`L_2/L_1`
`(L_2/L_1)^3`

ANSWER :D
Discussion
15661.

If particle stays at rest as seen from a frame of reference

Answer»

the frame may be inertial and a resultant FORCE ACTS on it
the frame may be non inertial and `F_("REAL")=-F_("pseudo")`
the FRAM may be non inertial but a resultant force acts on it
the frame must always be inertial

Answer :B
Discussion
15662.

A stone is thrown horizontally with velocity g ms^(-1) from thetop of a tower of height g metre . The velocity with which it hits the ground is ( in ms^(-1))

Answer»

G
2 g
`SQRT(3)` g
4g

Answer :C
Discussion
15663.

A shell is fired from a point O at an angle of 60^(@) with a speed of 40 m//s & strikes a horizontal plane throught O, at a point A. The gun is fired a second time with the same angle of elevation but a different speed v. If it hits the target which starts to rise vertically from A with a constant speed 9sqrt(3) m//s at the same instant as the shell is fired, find v.

Answer»


SOLUTION :RANGE `(OA)=(u^(2) sin 2 theta)/(g)=(1600 xx sqrt(3))/(10 xx 2)=80 sqrt(3)`
`h = 80 sqrt(3) xx tan 60^(@) = (10 xx 80 xx 80 xx 3)/(2 xx v^(2) COS 60^(@))`
Time to strike `rArr v cos60^(@) xx t = 80 sqrt(3)`
`rArr t =(80 sqrt(3) xx2)/(v xx1) =(10 sqrt(3))/(v)`
`h=9 sqrt(3) xx (160 sqrt(3))/(v) (480 xx 9)/(v) = (240^(2) - 38400)/(v^(2))`
`v^(2) -1600 - 18V =0`
`v =(18 PM sqrt(324)+6400)/(2)`
`rArr v =50 m//s`.
Discussion
15664.

Distinguishscalar and vector.

Answer»

SOLUTION :
Discussion
15665.

The sum of the magnitude of two forces acting at a point is 18 and them agnitude of their resultant is 12N. If the resultant is at 90^(@) with the smaller force of smaller magnitude , what are the magnitude of forces.

Answer»


ANSWER :5N,13N
Discussion
15666.

Water equivalent of a body is equivalent to the product of ……….. And ………….. Of the body

Answer»

SOLUTION :MASS , SPECIFIC HEAT
Discussion
15667.

The gravitational force between two particles of masses m_1 and m_2separated by certain distance in air medium is F. If they are taken to vaccum and separated by the same distance, then the gravitational force between them will be

Answer»

GREATER than F
LESS than F
F
Zero

Answer :C
Discussion
15668.

In the above problem velocity after 3 seconds is _______

Answer»

`20 HAT(i) + 20 sqrt(3)hat(j)`
`30hat(i)`
`10sqrt(3)hat(j)`
`30sqrt(3)hat(i)`

ANSWER :D
Discussion
15669.

A car window pane of length 25 cm is hinged at the top and 5 cm of its lower portion is covered by a fixed pane. Calculate the maximum anlgle by which the window pane can be raised outward without letting rain water enter into the car when it races through rain ( falling vertically at 20 kmph) at 60 kmph.

Answer»


ANSWER :`alpha=59^(@)`
Discussion
15670.

If a fluid flows through the narrower region of a tube of non-uniform cross section, then in that region of the tube

Answer»

both the VELOCITY and the PRESSURE of the FLUID will INCREASE
both the velocity and the pressure of the fluid will DECREASE
velocity of the fluid will decrease but pressure will increase
velocity of the fluid will increase but pressure will decrease

Answer :D
Discussion
15671.

The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 xx 10 ^(-11) Pa ^(-1)and density of water is 10 ^(3) kg//m^(3).What fractional compression (Delta V)/(V) of water will be obtained at the bottom of the ocean? (Take g = 10 ms ^(-2))

Answer»

`1.2 xx 10 ^(-2)`
`1.4 xx 10 ^(-2)`
`0.8 xx 10 ^(-2)`
`1.0 xx 10 ^(-2)`

Solution :The excess pressure at the bottom of ocean
`Delta P = h rho G`
`= 2700 xx 10 ^(3) xx 10 `
`= 27 xx 10 ^(6) Pa`
Bulk modulus `B = | (Delta P )/((Delta V )/(V ))|`
`therefore (Delta V)/(V) = (Delta P)/(B)`
`= Delta PK[because (1)/(B) =K]`
`=45.4 xx 10 ^(-11) xx 27 xx 10 ^(6)`
`=1225.8 xx 10 ^(-5)`
`~~1.2 xx 10 ^(-2)`
Discussion
15672.

A copper rod of length 60 cm long and 8 mm in radius is taken and its one end is kept in boiling water and the other end in ice at 0^(@) C. If 72 gm of ice melts in one hour with is the thermal conductivity of copper ? Latent of fusion of ice = 336 "KJ/Kg".

Answer»


SOLUTION :`K = m angle A ( theta_1 - theta_2) , t= 72xx 10^(-3) xx 336 xx 10^(-3) xx 0.60//pi xx (8 xx 10^(-3) )^(2) xx 100 xx 3600 = 200.64 "WM"^(-1) "K"^(-1)`
Discussion
15673.

n moles of an ideal monoatomic gas undergoes a process in which the temperature changes with volume as T = KV^2. If the temperature of the gas changes from T_0 to 4T_0then :

Answer»

WORK DONE by the GAS is `3nRT_0`
Heat SUPPLIED to the gas is `6nRT_0`
Work done by the gas is `3/2 nRT_0`
Heat supplied to the gas is `3/2 nRT_0`

Answer :B::C
Discussion
15674.

Three equal masses m are placed at the three vertices of an equilateral triangle of side a. The gravitational force exerted by this system on another particle of mass m placed at the mid point of a side

Answer»

`(Gm^2)/(3a^2)`
`(4Gm^2)/(3a^2)`
`(Gm^2)/a^2`
`(Gm^2)/(3a^2)`

ANSWER :B
Discussion
15675.

A space -ship is stationed on Mars. How much energy must be expended onthe spaceship to rocket it out of the solar system ? Mass of the spaceship = 1000 kg , Mass of the sun =2xx10^30 kg . Mass of the Mars = 6.4xx10^23 kg , Radius of Mars= 3395 km. Radiusof the orbit of Mars =2.28xx10^11 m, G=6.67xx10^(-11) Nm^2 kg^(-2)

Answer»

Solution :LET R, be the radius of orbit of Mars and R. be theradius of the Mars. M be the mass of the SUN and M. be the mass of Mars. If m is the mass of the space ship , then Potential energy of space ship due to gravititional attraction of the Sun = -GMm/R
Potential energy of space-ship due to gravititional attraction of Mars= -GM.m/R.
Since the K.E. of space-ship is zero, THEREFORE , total energy of space-ship
`=-(GMm)/R-(GM.m)/(R.)=-GM(M/R+(M.)/(R.))`
`therefore` Energy required to rocket out the SPACESHIP from the solar system =-(total energy of spaceship)
`=-[-Gm (M/R+(M.)/(R.))]=Gm (M/R+(M.)/(R.))`
`=6.67xx10^(-11)xx1000xx[(2xx10^30)/(2.28xx10^11)+(6.4xx10^23)/(3395xx10^3)]`
`=6.67xx10^(-8) [20/(2.28)+6.4/33.95]xx10^18` J = `5.98xx10^11` J
Discussion
15676.

A pank P is placed on a hollow cylinder C, which rolls on a horizontal surface as shown. No slippage is there at any the surface in contact Both have equal mass M each, and if is the velocity of centre of mass of the cylinder C, then the ratio of the kinetic energy of plank P to that of the cylinder C is x:1 where 'x' is

Answer»


ANSWER :2
Discussion
15677.

At what distance from the centre of Earth, the value acceleration due to gravity 'g' will be half that of the surface?

Answer»

SOLUTION :ACCORDING to acceleration due to gravity
` (G.)/g = (R/(R+h))^(2)`
`1/2 = (R/(R+h))^(2) RARR 1/(sqrt(2)) = R/(R+h)`
`R + h = sqrt(2)R rArr h = (sqrt(2)-1) R `
` h = 0.414 R `
Hencedistancefrom centre` = R + 0.414 R = 1.414 R `
Discussion
15678.

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to 1/3rd the escape velocity for the planet. The maximum height attained by the body is

Answer»

`R//2`
`R//3`
`R//5`
`R//9`

SOLUTION :Let `h` be the MAXIMUM HEIGHT ATTAINED, then from equation of the motion
`v^(2)=u^(2)+2gh`
when `u=0rArrv=sqrt(2gh)`
Given, `v=(v_(e))/(3)`, where, `v_(e)=sqrt(2gR)rArr sqrt(2gh)=(1)/(3)sqrt(2gR)`
On squaring both sides of equation, we get
`h=(R)/(9)`
Discussion
15679.

For measuring temperatures in the range of 2000°C,we should employ,

Answer»

GAS thermometer
Platinum-resistance thermometer
Barometer
Total RADIATION Pyrometer

Answer :D
Discussion
15680.

A 60 cm long granite rod is fixed at its midpoint and then longitudinal waves are set up in it. Find fundamental frequency of these waves. Density of granite is 2.7 xx 10^(3) kg/m3 and its Young modulus is 9.27 xx 10 ^(10) Pa.

Answer»

(A) 5 kHz
(B) `2.5 kHz`
(C) `10 kHz`
(D) `7.5kHz`

SOLUTION :Here speed od longitudinal wave, `v - sqrt ((Y)/(rho ))`
`therefore v = sqrt (( 9.27 xx 10 ^(10))/( 2.7 xx 10 ^(3))) = 5860 (m)/(s)`
Now, `v =f _(1) lamda_(1)`
(Where `f _(1)` = FUNDAMENTAL FREQUENCY)
`therefore v = f _(1) (2L) (because lamda _(n) = (2L)/(n ) and ` here `n =1 )`
`therefore f _(1) = (v)/(2L) = (5860)/(2 xx 0.6) = 4880 Hz ~~5 kHz`
Discussion
15681.

A conducting cylindrical rod of uniform cross-sectional area is kept between two large chambers which are at temperatures 100^(@)C and 0^(@)C, respectively. The cconductivety of the rod increases with x, where x is distance from 100^(@)C end. The temperature profile of the rod in steady -state will be as

Answer»




ANSWER :B
Discussion
15682.

Depth of water in a large container is 1000 cm. Water flows out with a rate of 5 It/s through an orifice near the bottom of the container. Calculate the rate at which water will escape through the orifice if an additional pressure of 20 kg f/cm""^(2) is applied at the surface of the water.

Answer»


ANSWER :23 lt/sec
Discussion
15683.

A hose pipe lying on the ground shoots a stream of water upward at an angle 60^(@)to the horizontal at a speed of 20ms^(-1). The water strikes a wall 20 m away at a height of (g=10ms^(-2))

Answer»

14.64 m
7.32 m
29.28 m
10 m

Answer :A
Discussion
15684.

A block of mass 6kg is lowered with the help of a rope of negligible mass through a distance of 20m with an acceleration of 1.96ms^(-2). Word done by the rope on the block is

Answer»

940.8J
470.4J
235.2J
`-940.8J`

ANSWER :D
Discussion
15685.

Which of the following is dimensionless A) Boltzmann constant B) Planks constant C) Poissons ratio D) Relative density

Answer»

Both A & B
Both B & C
Both C & D
Both D & A

Answer :C
Discussion
15686.

Two blocks A and B of the same mass and surface finish are sliding on the same surface. Area of contact of A is twice that of the B. The frictional force between A and the surface is

Answer»

TWICE that of B
half that of B
same that of B
depends on the POWER SUPPLIED

Answer :C
Discussion
15687.

Of the following the fastest process of heat transfer is

Answer»

conduction
convection
RADIATION
conduction through SILVER ROD

Answer :C
Discussion
15688.

The S.I unit of a physical quantity is [J.m^(-2)]. The dimensional formula for that quantity is

Answer»

`M^(1)L^(-2)`
`M^(1)L^(0)T^(-2)`
`M^(1)L^(2)T^(-1)`
`M^(1)L^(-1)T^(-2)`

ANSWER :B
Discussion
15689.

The momentum of a particle is vecP=costhetahati+sinthetahatj. The angle between momentum and the force acting on a body is

Answer»

`0^(@)`
`45^(@)`
`90^(@)`
`180^(@)`
Discussion
15690.

It is decided to verify Boyle's law over a wide range of temperature and pressures. The most suitable gas to be selected for this purpose is

Answer»

CARBON DIOXIDE
Helium
Oxygen
Hydrogen

ANSWER :D
Discussion
15691.

A refrigerator, whose coefficient of performance K is 5, extracts heat from the cooling compartment at the rate of 250 J per cycle.How much work per cycle is required to operate the refrigerator cycle ?

Answer»

Solution :As coefficient of performance of a REFRIGERATOR is DEFINED as `K = Q_L//W`.
so ` W= (Q_L)/(K )= ( 250)/(5) = 50J`
Discussion
15692.

Amonkey of mass 15kg is climbing on a rope with one end fixed to the ceiling. If it wishes to go up with an acceleration of 1m//s^2, how much force should it apply to the rope ? If the rope is 5m long and the monkey starts from rest, how much time will it take to reach the ceiling ?

Answer»

`120N , sqrt10 SEC `
`132 N, sqrt10sec`
`153N, sqrt10 sec `
`165 N, sqrt10 sec`

Answer :D
Discussion
15693.

A body travels uniformly a distance (13.8+-0.2) m in a time (4.0+- 0.3) s. Calculate its velocity with error limits. What is the percentage error in velocity ?

Answer»

Solution :Given DISTANCE, `s = (13.8 +-0.2) m` and time `t=(4.0 +- 0.3) s`
VELOCITY `v=(s)/(t)= (13.8)/(4.0)= 3.45 m s^(-1)`
`(Deltav)/(v)= +- ((Deltas)/(s)+(DELTAT)/(t))= +- ((0.2)/(13.8)+ (0.3)/(4.0))`
`= +- ((0.8 +4.14)/(13.8 xx 4.0))= +- (4.49)/(13.8 xx 4.0)= +-0.0895`
`Deltav=+0.0895 xx V= +-0.0895 xx 3.45 = +- 0.3087= +-0.31`
HENCE `v= (3.5 + -0.31) m s^(-1)`
Percentage error in velocity = `(Deltav)/(v) xx 100 = +0.0895 xx 100 =+- 8.95% = +- 9%`
Discussion
15694.

The minimum speed with whicih a body must be thrown to reach a height R/4 above the surface of the earth is (Rto Radius of the earth )

Answer»

`SQRT((GR)/(2))`
`sqrt(gR)`
`sqrt((2gR)/(5))`
`sqrt((gR)/(5))`

Answer :C
Discussion
15695.

Let P_(1) and P_(2) be the pressures above and below the water meniscus in a capillary tube, then

Answer»

<P>`P_(1)=P_(2)`
`P_(1)gtP_(2)`
`P_(1)ltP_(2)`
`P_(1)=P_(2)=0`

ANSWER :B
Discussion
15696.

A large steel wheel is to be fitted on to a shaft of the same material. At 27^(@)C, the outer diameter of the shaft is 0.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using 'dry ice'. At what temperature of the shaft does the wheel slip on the shaft ? Assume coefficient of linear expansion of the steel to be constant over the required temperature range : alpha_("steel")=1.20xx10^(-5)K^(-1).

Answer»

SOLUTION :Let `d_(1)` and `d_(2)` be the diameters of wheel at temperatures, `T_(1)` and `T_(2)` respectively.
`:.d_(2)=d_(1)[1+ALPHA(T_(2)-T_(1))]`
`:.d_(2)-d_(1)=d_(1)alpha(T_(2)-T_(1))`
`:.8.69-8.70=8.70xx1.20xx10^(-5)xx(T_(2)-300)`
`-0.01=8.70xx1.20xx10^(-5)xx(T_(2)-300)`
`:.T_(2)-300=(-0.01)/(8.7xx1.2xx10^(-5))`
`:.T_(2)-300=-95.78`
`:.T_(2)=300-95.98`
`:.T_(2)=204.22K`
`:.T_(2)~~204K`
`:.t_(2)=T_(2)-273`
`=204-273`
`=-69^(@)C`
Discussion
15697.

F=(Gm_(1)m_2)/r^2 is valid

Answer»

Between BODIES with any SHAPE
Between particles
Between any bodies with UNIFORM density
Between any bodies with same shape

ANSWER :A
Discussion
15698.

A police van moving on a highway with a speed of 30 km h^(-1) fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h^(-1). If the muzzle speed of the bullet is 150 ms^(-1), with what speed does the bullet hit the thief’s car ? (Note: Obtain that speed which is relevant for damaging the thief’s car).

Answer»

SOLUTION :`105 MS^(-1)`
Discussion
15699.

A solid cylinder of mass M and radius R can rotate about a horizontal axis. A long but light cord is wound over the surface of the cylinder and a mass m is suspended from its free end. Ifthe mass is released from rest what will be its acceleration ? Also determine the tension in the cord.

Answer»


ANSWER :`(2MG)/(M+2m),(MMG)/(M+2m)`
Discussion
15700.

A body is projected horizontal from the top of a hill with a velocity of 9.8 m/s.What time elapses before the vertical velocity is twice the horizontal velocity ?

Answer»

0.5 sec
1 sec
2 sec
1.5 sec

Answer :C
Discussion