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37751.

The velocity-time graph of a particle in one-dimensional motion is shown in the figure. Which of the following formulae is correct for describing the motion of the particle over the time interval t_1" to "t_2?

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`X(t_(2))=x(t_(1))+V(t_(1)) (t_(2)-t_(1))+(1/2)a(t_(2)-t_1)^(2)`
`v(t_(2))=v(t_(1))+a(t_(2)-t_(1))`
`v_("AVERAGE")=(x(t_(2))+x(t_(1)))/(t_(2)-t_(1))`
`a_("average")=(v(t_(2))-v(t_(1)))/(t_(2)-t_(1))`

ANSWER :D
37752.

The M.I. of a body is 1.2kgm^(2). Initially the body is at rest. In order to produce a rotational kinetic energy of 1500J an angular acceleration of 25rads^(-2) must be applied about the axis for a duration of

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`2S`
`4S`
`8S`
`10S`

ANSWER :A
37753.

Which of the following are positive and which are negative work done ? Work done by the resistive force of air on an oscillating pendulum in bringing it to rest.

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SOLUTION :NEGATIVE
37754.

Of the following the dimensionless error is

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SYSTEMATIC error
Gross error
random errors
Relative error

Answer :D
37755.

force F = 100 N is applied horizontally on a block of mass 4 kg. Which is in contact with a wall. Such that it does not fall. The coefficient of friction between the block and the wall is

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0.8
0.5
0.4
0.3

Solution :`N= mu_(s )F`
`mu_(s ) = (N )/( F ) =(mg )/(F ) = (4xx 10)/( 100) = 0.4`
37756.

Mass of the earth is 81 times that of the moon. If the distance between their centers is d, then the point on the line joining their centers at which the gravitational field due to them is zero is

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`d/10` from the CENTER of EARTH
`d/10` from the center of MOON
`(9d)/10` from the center of moon
`(d)/2` from each other

ANSWER :A
37757.

A car moving with a speed of 50 km/hr can be stopped by brakes after atleast 6m. If the same car is moving at a speed of 100 km/hr the minimum stopping distance is

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12 m
18 m
24m
6m

Answer :C
37758.

A person is sitting in a travelling train and facing the engine. He tosses up a coin and thhe coin falls behind him. It can be concluded from this that the train is

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moving forward and gaining SPEED
moving forward with uniform speed
moving forward and LOSING speed
moving backward with uniform speed

Solution :(a) is the correct STATEMENT.
The TRAIN is moving forward and gaining speed. The coin falls behind him with an acceleration 'g'.
37759.

(A) : Viscosity of a liquid is the property of the liquid by virtue of which it opposes the relative motion amongst its differents layers. (R ) : The viscosity of liquid increases rapidly with rise of temperature.

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Both (A) and (R ) are true and (R ) is the CORRECT EXPLANATION of (A)
Both (A) and (R ) are true and (R ) is not the correct explanation of (A)
(A) is true but (R ) is FALSE
Both (A) and (R ) are false

Answer :C
37760.

A referigertor has COP of 3 . How much work must be supplied to a refrigertor in order to remove 200J of heart from its interior?

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66.00 J
65.66 J
66.67 J
60 J

Solution :`COP = beta = (QL)/(W) RARR w = (QL)/(COP)=(200)/(3)=66.67J`
37761.

A particle is acted upon by constant magnitude force perpendicular to it which is always perpendicular to velocity of particle. The motion is taking place in a plane it follows that:

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velocity is constant
acceleration is constant
kinetic energy is constant
it moves in CIRCULAR path

Answer :C::D
37762.

A Steel tank is filled with a gas at 150 atmosphere and at 20^(@)C. If the pressure raise to 250 atmospheres, the tank explodes. Find the temperature at which the tank explodes

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`215.3^(@)C`
`273.3^(@)C`
`100.3^(@)`C
`373.3^(@)C`

ANSWER :A
37763.

Give dimensional formula of impulse of force.

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SOLUTION :`M^(1) L^(1)T^(1) ` Impulseof FORCE= variableof force
`= m Delta v`
37764.

A pipe, 30.0 cm long. Is open at both ends. Which harmonic mode of the pipe resonates a 1.1 kHz source? Will resonance with the same source be observed if one end of the pipe is closed ? Take the speed of sound in air as 330 m s^(-1).

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Solution :The first HARMONIC frequency is given by
`v_(1) = (v)/(lamda_(1)) = (v)/(2L)` (open pipe)
where L is the length of the pipe. The frequency of its nth harmonic is:
`v_(n) = (nv)/(2L)`, for n = 1,2,3. ……….(open pipe)
First few modes of an open pipe are shown in Fig. 15.15.


For L = 30.0 cm, `v = 330 m s^(-1)`,
`v_(n) = (n 330 (m s^(-1)))/(0.6 (m)) = 550 n s^(-1)`
Clearly , a source of frequency 1.1 kHz will resonate at `v_(2)`, i.e. the second harmonic.
Now if one of the pipe is closed (Fig. 151.15).
it FOLLOWS from Eq. (14.50) that the fundamental frequency is
`v_(1) = (v)/(lamda_(1)) = (v)/(4L)` (pipe closed at one END)
and only the ODD numnbered harmonics are present :
`v_(3) = (3v)/(4L), v_(5) = (5v)/(4L)`, and so on.
For L = 30 cm and `v = 330 ms^(-1)`, the fundamental frequency of the pipe closed at one end is 275 Hz and the source frequency corresponds to its fourth harmonic. Since this harmonic is not a possible mode, no resonance will be observed with the source, the moment one end is closed.
37765.

The time of flight is . . . . .the time taken to attain the maximum height .

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thrice
same
twice
four times

Answer :C
37766.

The time period of a satellite of earth is 5 hours . If the separation between earth and the satellite is increased to 4 times the previous value , the new time period will become

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`10HR`
`80hr`
`40hr`
`20HR`

ANSWER :C
37767.

The circular scale of a screw gauge has 50 divisions and pitch of 0.5 mm. Find the diameter of sphere. Main scale reading is 2 -

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`1.2`
`1.25`
`2.207`
`2.25`

Solution :LEAST COUNT `= (0.5)/(50) = 0.01 mm`
DIAMETER of sphere
`= 2 xx 0.5 + (25 -5)xx 0.01 = 1.2 mm`
37768.

A ball is thrown vertically upward with a velocity 'u' from the balloon descending with velocity v. After what time, the ball will pass by the balloon?

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Solution :`S_(R)=u_(r)t+(1)/(2)a_(r)t^(2)`
`O=(v+u)t-(1)/(2)g t^(2) t=(2(v+u))/(g)`
37769.

Give the quantities for which the following are the dimensions: M^(0)L^(0)T^(-2)

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ANSWER :ANGULAR ACCELERATION
37770.

A man standing inside a room of length L rolls a ball along the floor at time t = 0. The ball travels at constant speed v relative to the floor, hits the front wall (B) and rebounds back with same speed v. The man catches the ball back at the wall A at time t_(0). The ball travelled along a straight line relative to the man inside the room. Another observer standing outside the room found that the entire room was travelling horizontally at constant velocity v in a direction parallel to the two walls A and B. (a) Find the average speed of the ball in the time interval t = 0 to t = t_(0) as observed by the observer outside the room. (b) If the room hasacceleration in the direction of its velocity draw a sketch of the path of the ball as observed by the observer standing outside. Assume that velocity of room was vat the instant the ball was released.

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ANSWER :(a) `SQRT(2)v` (b) path is as SHOWN
`(##IJA_PHY_V01_C02_E01_132_A01##)`
37771.

The number of molecules of a gas in a container is doubled. What will be the effect on total energy of the gas.

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Solution :Total ENERGY = `3/2 Nk_BT`. When N is increased to 2N, total energy of the gas is DOUBLED.
37772.

A mass m attached to a spring oscillates with a period of 3 second. If the mass is increased by 2 kg, the period increases by one second. Calculate the initial mass m. (Assume that elastic limit is not crossed)

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SOLUTION :`3=2pisqrt(m//k) , 4 = 2pisqrt(m+2k),16//9=m+2//m ,=m = 18//7` KG
37773.

If x times momentum is work, then the dimensions. of x are

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`LT^(-1)`
`L^(-1) T`
`ML^(-1) T^(-1)`
`MLT`

Answer :A
37774.

The tube shown in of uniform cross section. Liquid lows through it at a constnat speed in te direction shown by the arrows. The liquid exerts on the tube.

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a net FORCE to the right
a net force to the left
a CLOCKWISE torque
an anticlockwise torque

Answer :C
37775.

The value of .g. at a particle point on the surface of the earth is 9.8ms^2 Suppose the earth suddenly shrinks uniformly to half its present size without losing any mass, the value of g at the same point (assuming that the distance of the point from the centre of the earth does not shrink) will now be:

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`4.9 MS^(-2)`
`3.1 ms^(-2)`
`9.8 ms^(-2)`
`19.6 ms^(-2)`

ANSWER :C
37776.

A body of mass 4 kg is moving with momentum of 8 kg m s^(-1). A force of 0.2 N acts on it in the direction of motion of the body for 10 s. The increase in kinetic energy is

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10 J
8.5J 
4.5 J
4J 

ANSWER :C
37777.

A force of 35N acts in the direction parallel to 2 hat(i) + 3hat(j) + 6hat(k) and it displaces a body from (1m, 0m, 3m) to (3m, 4m, 1m) find the work done

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20J
22J
11J
zero

Answer :A
37778.

How will you determine the direction of torque?

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Solution :The direction of torque is always perpendicular to the plane containing `vecr and vecF`. It is given by right hand RULE. CURL of FINGERS of the right hand in the sense that would ROTATE the first vector `vecr` into the SECOND vector `vecF` through the smaller angle. Then extended thumb gives the direction of torque.
37779.

A light thread is wound on a disk of mass 'm' and other end of thread is connected to a block of mass 'm', which is placed on a rough as shown in fig. The minimum value of coefficient of friction for which block remain at rest, is mu=1//x then x is __________

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ANSWER :3
37780.

Momentum and change in momentum are always in same direction.

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ANSWER :FALSE. Both NEED not to be in same DIRECTION.
37781.

A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire is so that speed of a transverse wave on the wire equals the speed of sound in dry air is343 ms ^(-1).

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Solution :Speed of TRANSVERSE wave in a wire is,
`v = sqrt ((T)/(mu)) = sqrt ((TL)/(M)) ""(because mu = (M)/(L))`
`therefore v ^(2) = (TL)/(M) implies T = (Mv ^(2))/(L) = ((2.1 ) (343) ^(2))/((12))=20588.575N`
`therefore T ~~2.06 xx 10 ^(4) N`
37782.

The length of a metal rod at 0^(@)C is 0.5m. When it is heated, its length increases, by 2.7 mm.The final temperature of the rod is (coefficient of linear expansion of the metal =90xx10^(-6)//^(@)C)……………. .

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`20^(@)C`
`30^(@)C`
`40^(@)C`
`60^(@)C`

Solution :`l_(t)=l_(0)(1+alphat)`
`therefore""t=(l_(t)-l_(0))/(l_(0)alpha)=(2.7xx10^(-3))/(0.5xx90xx10^(-6)), t=60^(@)`
37783.

A boy standing on a stationary lift (open from above) throws a ball upwards with the maximum initial speed he can, equal to 49 ms^(-1). How much time does the ball take to return to his hands ? If the lift starts moving up with a uniform speed of 5 ms^(-1) and the boy again throws the ball up with the maximum speed he can, how long does the ball take to return to his hands ?

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SOLUTION :10S, 10 s
37784.

What do the slope and the area under a vet graph represent?

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Solution :v-t GRAPH – slope = ACCELERATION and v- t graph - AREA = DISTANCE.
37785.

A ring, a disc and a sphere all of the same radius andmass roll down an inclined plane from the same height h. Which of the three reaches bottom (i) earliest (ii) latest ?

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Solution :The ACCELERATION attained by the centre of mass of a rolling body down an inclined plane is
`a =(g sin THETA)/(1 + I/(MR^(2))`
For a ring, `I = MR^(2), a_(r) (g sin theta)/2`
For a disc `I = 1/2 MR^(2), a_(d) = (g sin theta)/(1+1/2) = (2g sin theta)/3`
For sphere, `I = 2/5 MR^(2), a_(s) = (g sin theta)/(1 +2/5) = (5g)/7 sin theta`
Thus, `a_(r) lt a_(d) lt a_(s)`.They all start from rest. So the sphere will reach bottom FIRST and the ring last.
37786.

We are standing in a bus moving with constant velocity. When brakes are applied to bus we are thrown in forward direction ? Why ?

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Solution :WHENWE are standinginstationarybus ourfeetare intouchwiththe FLOOR.
Frictionalforceis betweenfeetand floorof thebus.
Whenbussuddenlystartdueto frictionourfeetstartmovingin directionof buswhereasrest OFTHE bodytryto retainpositiondue toinertia.
hencewe arethrownin backwarddirection inoppositedirection OFOF buswhereasrestofthe bodytryto retainpositiondue toinertia
hencewe arethrowninbackwarddirection inoppsitedirectionof accelerationof bus.
37787.

Calculate the amount of heat that must be supplied to 40 gm of nitrogen to raise its temperature by 45^(@)C at constant pressure if it is at room temperature. R = 8.3 J mol ^(-1) K ^(-1).

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<P>

Solution :`Delta Q = n C _(P) DT = (40 xx 10 ^(-3) //28 xx 10 ^(-3)) xx (7 R //2) xx 45 = 1867.5 J`
37788.

(A): The internal energy of an ideal gas does not change during an isothermal process (R ): In isothermal process product of pressure and volume is constant.

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Both (A) and(R ) are true and (R ) is the CORRECT explanation of (A)
Both (A) and (R ) are (R ) true and is not the correct explanation of (A)
(A) is true but (R ) is FALSE
Both (A) and (R ) are false

Answer :A
37789.

Particles of masses m_1 and m_2 are at a fixed distance apart . If the gravitational field strength at m_1 and m_2 are vecI_1 and vecI_2 respectively . Then ,

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`m_1 vecI_1 + m_2 vecI_2=0`
`m_1 vecI_2+m_2 vecI_1=0`
`m_1 vecI_1 - m_2vecI_2=0`
`m_1vecI_2-m_2vecI_1=0`

ANSWER :B
37790.

Which of the following option correctly describe the variation of the speed upsilon and acceleration 'a' of a point mass falling vertically in a viscous medium that applies a force F= - k upsilon, where 'k' is a constant, on the body ? (Graphs are schematic and not drawn to scale)

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ANSWER :D
37791.

A spherical ball of radius r and relative density 0.5 is floating in equilibrium in water with half of it immersed in water. The work done in pushing the ball down so that whole of it is just immersed in water is : (where is the density of water)

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`(5)/(12) PI R^(4) rho g`
`0.5 rho g`
`(4)/(2) pi rhog`
`(2)/(3) pi r^(4) rhog`

Answer :A
37792.

body is allowed to fall from a height h above the ground. Then match the following

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a-e,b-g,c-h,d-f
a-g,b-e,c-f,d-h
a-f,b-g,c-end-h
a-e,b-h,c-g,d-f

ANSWER :A
37793.

Define intensity ofa wave.

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Solution :The average power transported by a wave PER unit surface area of the medium is KNOWN as the INTENSITY of the wave.
[Note `: I =( "Power")/("area") =2pi^(2) f^(2) A^(2) PV`.
where `rho`-DENSITY of the medium and v-velocity of the wave ].
37794.

A block of mass m placed on a rough inclined plane of inclination theta = 30^@ can just be prevented from sliding down by applying a force Fi up the plane and it can be just made to slide up the plane by applying a force F_2 up the plane. If the coefficient of friction between the block and the inclined plane is (1)/( 2 sqrt(2sqrt(3)) the relation between F_1and F_2 is

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`F_2 =4F_1`
`f_2 - 3F_1`
`F_2-2F_1`
`F_2 -F_1`

Solution :The FORCE`F_1`requiedto preventto blockfromslidingdownis
`F_1= mgsin theta- mumg cos theta `
The force` F_2`requiedto maketheblock moveupthe planeis
` F_2 = mgsintheta+ mu MG cos theta`
adding(i) and (II) , we get
` F_2 -F_1= 2 mu mgcostheta`
` therefore(F_2+F_1)/(F_2 -F_1) = ( 2 mgsin theta)/( 2 mumgcos theta) = ( tan theta)/( mu) = (tan 30^@)/(1 // 2 sqrt(3)) =2`
` orF_2 + F_1 = 2F_2 - 2F_1 `
` or 3F_1= F_2orF_2=3F_1`
37795.

The compensated pendulum of a clock consista of an isosceles triangular frame of base length l_(1) and expansivity alpha_(1) and side length l_(2) and expansivity alpha_(2). The pendulum is supported as shown in the figure. Calculate the ratio l_(1)//l_(2) so that the length of the pendulum may remain unchanged at all temperatures?

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Answer :`(l_(1))/(l_(2))=2 SQRT((alpha_(2))/(alpha_(1)))`
37796.

If lt E gt and lt U gt denote the average kinetic and the average potential energies respectively of mass describing a simple harmonic motion, over one period, then the correct relation is

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`LTE GT = ltUgt`
`ltEgt = 2ltUgt`
`ltE gt = -2ltUgt`
`ltEgt = -ltUgt`

ANSWER :A
37797.

The M.I of a thin circular disc about a tangent in the same plane of disc is I. Then M.I. about one of the diameters is

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`0.2I`
`0.8I`
`1.25I`
`2.5I`

ANSWER :A
37798.

Two block of masses 3 kg and 1 kg are kept in contact with rach other on a frictionless horizontal surface. If a force of 10 N is applied on the larger block what is the acceleration of the system ? What is the contact force between the two blocks ?

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`2.5 m//s^(2), 2.5 N`
`5 m//s^(2), 5N`
`5 m//s^(2), 2.5 N`
`2.5 m//s^(2), 5N`

ANSWER :A
37799.

What type of changes occur in a object by heating it ?

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Solution :When an object is heated, many CHANGES may TAKE place. Its temperature may RISE, it may EXPAND of change state.
37800.

Suppose a disc is rotating counter clockwise in the plane of the paper then

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It.s angular VELOCITY VECTOR will be perpendicular to the page POINTING up out of the page
It.s angular velocity vector will be perpendicular o the page pointing inwards
It.s agular velocity vector acts ALONG the tangent to the disc.
None of the above is correct.

Answer :A