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12651.

A wheel of moment of inertia 0.10" kg-m"^(2) is rotating about a shaf at an angular speed of 160 rev/minute. A second wheel is set rotation at 300 rev/minute and is coupled to the same shaft so that both the wheels finally rotate with a common angular speed of 200 rev/minute. The moment of inertia of the second wheel is (x)/(100)"kgm"^(2). then x is _______.

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ANSWER :4
12652.

The length of a metal wire is l_(1) when the tension in it is T_(1) and is l_(2) when the tension is T_(2). The natural length of the wire is:

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SOLUTION :`"From LENGTH expansion equation "(DeltaL)/(L)=alpha_(L)DeltaT`
`"From Area expansion equation, "((DeltaV)/(V_(o)))=alpha_(A)DeltaT`
But `alpha_(A)=2alpha_(L)`, therefore, `(DELTAA)/(A_(o))=2alpha_(A)DeltaT=2(DeltaL)/(L)`
Percentage CHANGE `=(DeltaA)/(A_(o))xx100=2((DeltaL)/(L)xx100)=2xx1`
Percentage change `=2%`
12653.

If a freely falling body covers half of its total distance in the last second of its journey. Find its time of fall.

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Solution :SUPPOSE t is the TIME of free FALL.
`h=1/2 gt^(2)……(1)`
`h/2=1/2 g(t-1)^(2)……..(2)`
Solving 1,2 `t=(2+sqrt2)s`
since `2-sqrt2` is not acceptable.
12654.

A bodyof mass 4 kg is connected to the two ends of a vertical rod of length 2 m by two threads of length 1.5 m each. The body is rotated about the rod as an axis. To produce a tension of 70 N on the upper string what should be the rpm of the body? What will be the tension in the lower string then?

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ANSWER :35.1 RPM, 11.2 N
12655.

Expansion during heating :

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OCCURS only in solids
increases the WEIGHT of a material
decrease the DENSITY of a material
occurs at the same RATE for all solids and liquids

Answer :C
12656.

A smooth pulley A of mass M_(0)is lying on a smooth table . A light string passes round the pulley and has masses M_(1) "and" M_(2)attached to its ends , the two portions of the string being perpendicular to the edge of the table so that the masses hang vertically . Calculate the acceleration of the pulley .

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SOLUTION :Let the length of portions of string on the table be `l_(0),l_(1) "and" l_(2) ` as shown in figure .
Let mass `M_(0)` move to the right by x on the table ,` M_(1) `goes down by `y_(1) "and" M_(2) ` goes up by `y_(2)`
Then `l_(0)` becomes `(l_(0)-x)` l_(1)` becomes `(l_(1)+y_(1))` and `l_(2) ` becomes `(l_(2)-y_(2))`.
As the length of string remains unchanged
`2l_(0)+l_(1)+l_(2)=2(l_(0)-x)+l_(1)+y_(1)+l_(2)-y_(2)`
or `2x=y_(1)-y_(2)`
Diff. twice w.r. to t,
we get `2(d^(2)x)/(dt^(2))=(d^(2)y_(1))/(dt^(2)-(d^(2)y_(2))/(dt^(2))`
If a_(0),a_(1)"and"a_(2)` are ACCELERATION of

`M_(0),M_(1)` and `M_(2)` respectively , then
`2a_(0)=a_(1)-a_(2)`....(1)
For motion of `M_(0),2T=M_(0)a_(0)`....(2)
For motion of mass `M_(1)`
`M_(1)g-T=M_(1)a_(1)`....(3)
For motion of mass `M_(2)`,
`T-M_(2)g=M_(2)a_(2)`....(4)
Substituting values of `a_(0),a_(1)` and `a_(2)` from (2) ,(3) and (4) in equation (1) , we get
`2((2T)/M_(0))=(g-T/M_(1)-(T/M_(2)-g),`
`(4T)/M_(0)=2g-T(1/M_(1)+1/M_(2)) `i.e., (4/M_(0)+1/M_(1)+1/M_(2))T=2g`
This gives `T=(2M_(0)M_(1)M_(2)g)/(4M_(1)M_(2)+M_(0)(M_(1)+M_(2))`....(5)
`:. ` Aceeleration of PULLEY A from (2)
`a_(0) =(2T)/M_(0)=(4M_(1)M_(2)g)/(4M_(1)M_(2)+M_(0)(M_(1)+M_(2))`....(6)
12657.

The relative density of the material of body is the ratio of it's weight in air and to the apparent loss of it's weight in water. By using a spring balance. The weight of body measured in air is (5.00+0.05) N. The weight of the body measured in water is found to be (4.00 pm 0.05) N.Then the maximum possible percentage error in relative density is

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`11%`
`10%`
`9%`
`7%`

ANSWER :A
12658.

Amplitude of a SHO is sqrt(5) cm. At what displacement fromthe mean position the ratio of kinetic energy to potential energy is 4?

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SOLUTION :`implies ("KINETIC energy")/("Potential energy")= 4`
Kinetic energy = 4 potential energy
`therefore (1)/(2)k(A^(2)-x^(2))= 4(1)/(2)KX^(2)`
`therefore A^(2)- x^(2) = 5x^(2)`
`therefore A^(2)= 5x^(2)`
`therefore x = pm (A)/(sqrt(5))= pm (sqrt(5))/(sqrt(5))= 1 CM`.
12659.

A car is moving with a constant speed on a straight line. State work energy theorem.

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SOLUTION :The CHANGE in kinetic ENERGY of a particle is EQUAL to the work done on it by the net force.
12660.

What is the net force on a piece of wood floating on water?

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SOLUTION :ZERO, because the weight of the wooden PIECE is balanced by the upward thrust or BUOYANCY of the LIQUID.
12661.

The magnifying power of a simple microscope can be increased, if we use an eye piece of

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HIGHER FOCAL length
Small focal length
Higher diameter
Smaller diameter

Answer :B
12662.

Heat flows radially outward through a spherical shell of outside radius R_(2) and inner radius R_(1). The temperature of inner surface of shell is theta_(1) and that of outer is theta_(2). At what radial distance from centre of shell the temperature is just half way between theta_(1) and theta_(2)

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`(3R_(1)+R_(2))/(2)`
`(4R_(2)+3R_(1))/(3)`
`(8R_(2)R_(1))/(4R_(1)+3R_(2))`
`(2R_(1)R_(2))/(R_(1)+R_(2))`

Answer :D
12663.

n moles of a gas expands from volume V_(1)toV_(2)at constant temperature T. The work done by the gas is

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`NRT( (upsilon_(2))/(upsilon_(1)))`
`nRT ((upsilon_(2))/(upsilon_(1))-1)`
`nRT " In"((upsilon_(2))/(upsilon_(1)))`
`nRT" In "((upsilon_(2))/(upsilon_(1))+1)`

ANSWER :C
12664.

A block of mass m =5kg is dropped onto a masless pan attached to a spring of constant k-200N/m from a height h. The second end of the spring is attached to a second block of mass M=10Kg as shwon. The minimum value of h so that the block M bounces of the ground if the block m sticks to the pan immediately after it comes in contact with it (g=10m//s^(2))

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1m
2m
3m
4m

Answer :A
12665.

Balloon has 5 mole of helium at 7^@C. The total internal energy of the system is

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`1.74 XX 10^(4)J`
`1.74 xx 10^(-4)J`
`0.74 xx 10^(4)J`
`1.74 xx 10^(8)J`

ANSWER :A
12666.

Two blocks A and B each of equal masses m are rleased from the top of a smooth fixed wedge as shown in the figure. Find the magnitude of the accelertion of the centre of mass of the two blocks.

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Solution :Let US consider incline surfaces of wedge as `x`-axis and `y`-axis respectively. We can write accelerations of BLOCKS `A` and `B`.

`veca_(A)=mg sin 30^(@) hati` and `veca_(B)=mg cos 30^(@)hatj`
The acceleration of centre of mass of two blocks can be written as
`veca_(cm)=(m_(A)veca_(A)+m_(B)veca_(B))/(m_(A)+m_(B))=(mgsin30^(@)hati+mgsin60^(@)hatj)/(m+m)`
`(gsin30^(@)hati+gsin60^(@)hatj)/2`
`=g/4hati+(SQRT(3)g)/4hatjimplies |veca_(cm)|=g/2`
12667.

If linear momentum of a body is increased by 0.5% its kinetic energy increases b y ..

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0.1
0.01
0.02
0

Solution :`1 %`
`k= (p^(2))/( 2M )` WHERE2 m ISEQUAL
`k= P^(2)`
`(Delta k )/( k ) = (2Delta p )/( p )`
`(Delta k )/( k ) xx 100= 2xx (Delta p ) /( p ) xx 100`
`=2 xx 0.5 %`
`=1.0 %`
12668.

For a particle revolving in a circular path, the acceleration of the particle is

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ALONG the TANGENT
along the RADIUS
along the CIRCUMFERENCE of the circle
zero

SOLUTION : along the radius
12669.

(A) : Air flows from a small bubble to a large bubble when they are connected to each other by a capillary tube. (R ) : The excess pressure because of surfaces tension inside a spherical bubble decreases as its radius increases.

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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 :A
12670.

A wheel is rolling on a horizontal plane. At a certain instant it has a velocity 'v' and acceleration 'a' of CM as shown in fig acceleration of

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A is vertically upwards
B may be vertically downwards
C cannot be horizontal
Some POINT on the rim may be horizontal left wards

Answer :A::B::C::D
12671.

A carnot engine operating between temperature T_(1) andT_(2) has efficiency (1)/(6). When T_(2) is lowered by 62 K, its efficiency increases to (1)/(3). Then find the values of T_(1) and T_(2).

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Solution :`"Efficiency"eta=1-(T_(2))/(T_(1))`
`"In the first case :"1-(T_(2))/(T_(1))=(1)/(6) rArr (T_(2))/(T_(1))=(5)/(6)`
`T_(1)=(6)/(5)T_(2)`
`"In the SECOND case :"1-((T_(2)-62))/(T_(1))=(1)/(3),(T_(2)-62)/(T_(1))=(2)/(3)`
`(T_(2)-62)/(((6)/(5))T_(2))=(2)/(3)`
`T_(2)-62=(2)/(3)XX(6)/(5)T_(2)=(4)/(5)T_(2)rArr T_(2)=310K`
`T_(1)=(6)/(5)xx310=372K`
`T_(1)=372K and T_(2)=210K.`
12672.

A planet revolvesround the sun in an elliptical orbit of minor axes x and y respectively. Then the time period of revolution is proportional to

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`(X +y)^(3//2)`
`(y-x)^(3//2)`
`x^(3//2)`
`y^(3//2)`

ANSWER :D
12673.

The number of significantdigita in 0.002 is

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1
2
3
4

Answer :A
12674.

A man wants to draw a bucket full of water in two different ways. As shown in figure 'a' he draws the bucket directly and as shown in figure (b) he uses a pulley. The weight of the man is 50kg and the bucket with full water weighs 25kg. Find the action on the floor by the man in the two cases. (Take g=10ms^(-2)).

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ANSWER :(a) 750 N; (B) 250N
12675.

Choose the odd man out.

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Helium is a monoatomic GAS
Methane is a polyatomic gas
Neon is an INERT gas
Oxygen is a DIATOMIC gas

Solution :STATEMENT is not related to the number of atoms in Neon.
12676.

What is meant by a cyclic process ?

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SOLUTION :A cyclic PROCESS is a succession of changes that ends with the RETURN of the thermodynamic system to its INITIAL state.
12677.

If the terminal speed of a sphere of gold (density = 19.5 gmcm^(-3) is 0.2 m/s in a viscous liquid, (density =1.5gmcm^(-3) the terminal speed of a sphere of silver (density = 10.5 gmcm^(3) of the same Size in the same liquid is.

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`0.1ms^(-1)`
`0.225ms^(-1)`
`0.225cms^(-1)`
`0.133ms^(-1)`

ANSWER :A
12678.

A massless string passes over a frictionless pulley and carries mass m_1 hanging at one end and mass m_2 connected by another massless string to mass m_3 at other end as shown in figure. Calculate the tension in string joining masses m_2 and m_3.

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Solution : Let `T_1` be the tension in the string joining `m_1 and m_2`, while `T_2` the tension is string joining `m_2 and m_3`.
Let a be acceleration of MASSES. The resultant force on mass `m_3` is `(m_3g-T)` downward, therefore, we have
`m_3g - T_2 = m_3a` ......... (1)
Resultant force on mass ` m_2 ` is
` (m_2 g + T_2-T_1)` downwards , therefore , we have
`m_2 g + T_2-T_1 = m_2 a ` ...... (2)
Reusultant force on mass ` m_1 ` is ` (T_1 - m_1 g )` upward , therefore , we have
` T_1 -m_1 g = m_1 a ` ........ (3)
Adding (1) , (2) and (3) , we get , `m_3g + m_2g - m_1 g = (m_3 + m_2 + m_1) a `
`:. ` acceleration ` a=((m_2 + m_3-m_1))/( m_1 + m_2 + m_3) g `
substituting this value of a in (1) , we get
`m_3 g - T_2 = m_3 . ((m_2 + m_3 - m_1)g)/(m_1 + m_2 + m_3)`
This gives `T_2 = m_3 g - (m_3 (m_2 + m_3 - m_1)g)/( m_1 + m_2 + m_3)`
`:. ` Requried Tension , `T_2 =(2m_1 m_3 g)/( m_1 + m_2 + m_3)`.
12679.

A,B and C are three optical media of respective critical angles.C_1,C_2 and C_3 Total internal reflection of light can occur from A to B and also from B to C but not from C to A. Then the correct relation between critical angles is

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`C_1 GT C_2 gt C_3`
`C_1=C_2=C_3`
`C_3 gt C_1 gt C_2`
`C_1 LT C_2 lt C_3`

ANSWER :D
12680.

{:(,"List - I",,"List - II"),((a),"Impulse",(e ),"elastic collision"),((b),"coefficient of restitution",(f),"changeing momentum"),((c ),"conservation of momentum",(g),"relative velocity of seperation / relative velocity of approach"),((d),"conservation of kinetic energy",(h),"internal force"):}

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

Answer :B
12681.

A solid sphere , a hollow sphere and a disc , all having same mass and radius , are placed at the top of an incline and released . The friction coefficient between the objects and the incline are same and not sufficient to allow pure rolling . Prove that time taken in reaching the bottom is same for all .

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Solution :As the body does not undergo pure rolling , it means friction acting is kinetic friction = `mu N` .
Normal to the inclined plane , the body is in equilibrium , hence

N = `Mg COS theta`
Along the inclined plane ,
`Mg sin theta - mu N = Ma implies Ma = Mg sin theta - mu Mg cos theta`
or `a = G sin theta - mg cos theta`
As MOMENT of INERTIA , does not feature in the acceleration equation , all bodies whether they are SOLID sphere , hollow sphere or disc will have the same acceleration . they will take the same time to reach the bottom .
12682.

A typicalstar is a spherical ball withheat sourceparticipatingin thephenomenon of heatgeneration at asteadyrate , spread from unifromly , throughout its volume. By whatfactor, woulditsthemodynamictemperaturechange , if itsradius be decreased byhalf ?

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SOLUTION :`(1//(2^(1//4)))`
12683.

The masses m_(1)=10 kg m_(2)=5 kg are connected by a ideal string as shown in figure. The coefficient of friction m_(1) and the surface is mu=0.2.Assuming that the system is released from rest. Calculate the velocity of block when m_(2) has descended by 4m? [g=10ms^(-2)]

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`2MS^(-1)`
`3MS^(-1)`
`4ms^(-1)`
`5MS^(-1)`

Answer :C
12684.

An isolated particle of mass 'm' is at rest in a horizontal plane (x-y) along the x-axis, at a certain height above the ground. It suddenly explodes into two fragments of masses m/4 and 3m/4, the speed of heavier fragments is V_(0) horizontally at the instant of explosion. At an instant t_(0) later, the smaller fragment is at y = y_(0) below the point of projection. Then

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The HORIZONTAL separation between the two fragments is `3V_(0) t_(0)` at that instant `t_(0)`
The horizontal separation between the two fragments is `2V_(0) t_(0)` at that instant `t_(0)`
The speed of the smaller fragment at the instant `t_(0)` is `sqrt(V_(0)^(2) + 2G y_(0))`
The speed of the smaller fragment at the instant `t_(0)` is `sqrt(9V_(0)^(2) + 2g y_(0))`

Answer :A::D
12685.

A block of mass m is placed on a smooth slope of angle theta. The whole system (slope + block) is moved horizontally with acceleration a in such a way that the block does not slip on the slope.Hence, a =………..

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`G tan theta`
`g sin theta`
`g COS theta`
`(g)/(sin theta)`

Solution :As blockdoenstslipon slope
`m a COSTHETA= mgsin theta `

` a= g(sin theta )/(cos theta )`
` a=g tan theta`
12686.

At what points along the path of a simple pendulum is the tension in the string maximum

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SOLUTION :The tension is minimum at either extreme POSITION and is EQUAL to MG`COS0`
12687.

Consider the following two statements. (A) Linear momentum of a system of particles is zero (B) Kinetic energy of a system of particles is zero. Then.

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A does not IMPLY B , B does not imply A
A implies B but B does not imply A
A does not imply B but B implies A
A implies B and B implies A

Answer :C
12688.

A remote sensing satellite is revolving in an orbit of radius x above the equator of earth. Find the area on earth surface in which satellite can not send message.

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Solution :
Area of STRIP =`2Rsin thetaxx2piR`
`=4piR^(2)SIN theta`
Area of strip`=4piR^(2)(sqrt(x^(2)-R^(2)))/x`
Area not covered `=4piR^(2)-4piR^(2)(sqrt(x^(2)-R^(2)))/x`
`=(1-(sqrt(x^(2)-R^(2)))/x) 4piR^(2)`
12689.

A second pendulum is shifted from Delhi to London . If the accelereation due to gravity at london is 981cm/s^(2) and increases in length of the pendulum is observed to be 0.2 cm , then the acceleration due to gravity at Delhi is

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`983cm/s^(2)`
`979cm/s^(2)`
`985cm/s^(2)`
`977cm//s^(2)`

Solution :Time period of pendulum is GIVEN by
`t = 2pisqrt((l)/(G))`
`RARR l = (gT^(2))/(4pi^(2))`
For second.s pendulum, T =2 s
`therefore l = (g(2^(2)))/(4pi^(2)) = (g)/(pi^(2))`
At London,
`therefore l = (g)/(pi^(2)) = (981)/(10) = 98.1` cm `(pi^(2) = 9.8696 ~~ 10)`
At Delhi, `therefore l = 0 .2 = (g.)/(pi^(2)) = (g.)/(10)`
`rArr g. - 10L - 2 = 10 xx 98.1 - 2 = 979 cm//s^(2)`
12690.

A force F is given byF=at+bt^2 where t is time. What are the, dimensions of a and b?

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SOLUTION :`[F]=[at]=[bt^2][a]=[[F]]/[[t]]=[[MLT^2]]/[[T]]=[MLT^-3][B]=[[F]]/[[t^2]]=[[MLT^2]]/[[T^2]]=[MLT^-4]`
12691.

A particle executing SHM of period 12 seconds moves through a distance of 32 cm in one oscillation. Find the time it takes to travel 4cm from the positive extreme of its oscillation,

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1 SEC
1.2 sec
2 sec
1.4 sec

ANSWER :C
12692.

A perfectly elastic ball P_(1) of mass m moving with velocity v collidies elastically with three exactly similar balls P_(2),P_(3),P_(4) lying on a smooth table as shown. Velocities of the four balls after the collision are

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V,v,v,v
0,2v,3v,4v
0,0,0,v
0,0,0,0

Answer :C
12693.

A flat-bottomed glass tube has a diameter of 4 cm and weighs 30gxxg. The centre of gravity of the empty tube is 10 cm above the bottom. Find the amount of water which must be poured into the tube so that when it is floating vertically in a tank of water, the centre of gravity of the system is at the mid-point of the immersed length of the tube.

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ANSWER :0.1107 KG (APPROX.)
12694.

A system consists of two identical particles one particle is at rest and the other particle has an acceleration .a.. The centre of mass if the system has an acceleration of

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2A
a
a/2
a/4

Answer :C
12695.

Explain why a piece of iron appears to be cooler than a piece of wood in winter.

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SOLUTION :IRON is a good conductor of heat while wood is a bad conductor if we touch a piece of iron and a piece of wood keep that a same temperature iron APPEARS cooler to the hand CAUSE it rapidly conducts more heat away from our BODY then the piece of wood.
12696.

Compare static friction and kinetic friction.

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SOLUTION :
12697.

The relation between position and time f for a particle , performingone dimensional motion is as under : t = sqrt(x) +3 Here x is in metre and t is in second . (1) Find the displacementof the particle when its velocitybecomes zero . (2) Ifa constant force acts on the particle , find the workdone in first 6 second .

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Solution :`t = sqrt(x)+3`
` :. x =(t-3)^(2)`
Now `v=(DX)/(dt) =2(t-3)`
At time t = 0 , velocity `v_(1)=-6 m//s `
At time t=6 velocity `v_(2) = 6 m//s `
` :. DeltaK = 1/2 mv_(2)^(2) - 1/2 mv_(1)^(2)`
` = 1/2 m [ (6)^(2)-(-6)^(2)] = 1/2 m [36 -36] `
` :. DeltaK = 0 "" :. "Work W = 0 "`
12698.

A particle of mass m moves along a circle of radius. R with a normal acceleration varying with time as a_(n) = kt^(2), where k is a constant. Find time dependence of power developed by all the forces acting on the particle and the mean value of this power averaged over the first T seconds after the beginning of the motion.

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Solution :Normal acceleration `a_(n) = KT^(2)`
`therefore (v^(2))/(R) = kt^(2) or (dv//dt) = sqrt((kR))`
We know that in circular motion, work done by normal FORCE is zero. For tangential forces
`F_(t) = m(dv//dt) = m sqrt((kR)),`
Now Power `P = VEC(F_(t)).vec(v) = F_(t).v cos theta = F_(t).v ""(because theta = 0) = mkRt`
Further,

`= (int_(0)^(T) P(t) dt)/(int_(0)^(T) dt) = (int_(0)^(T)m k R t dt)/(T) = (m k R[t^(2)//2]_(0)^(T))/(T) = (mkRT)/(2)`.

12699.

Which of the following statements is// are true for a simple harmonic oscillator ?

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Force acting is directly proportional to displacement from the mean position and OPPOSITE to it.
MOTION is periodic
Acceleration of the OSCILLATOR is constant
The VELOCITY is periodic

Solution :Knowledge BASED question.
12700.

The area of a glass window is 1.2 m^(2). The thickness of the glass is 2.2 mm. If the temperature outside is 36°C and the temperature inside is 26°, calculate the heat flowing into the room every hour. Thermal conductivity of glass is 0.8 Wm^(-1) K^(-1).

Answer»

Solution :Area `= A= 1.2 m^(2)`
Thickness of GLASS `= x = 2.2 " mm" = 2.2 xx 10^(-3) "m"`
Temperature difference `= theta_1 - theta_2 = 36 - 26 = 10^(@) C`
`= 10K`
THERMAL conductivity of glass = K
`=0.8 Wm^(-1) K^(-1)`
Time `= t =1` hour `= 3600 s`
Quantity of HEAT flowing in one hour `= ( KA ( theta_1 - theta_2 ) t)/( x ) = (0.8 xx 1.2 xx 10 xx3600)/( 2.2 xx 10^(-3) )`
`= 1.57 xx 10^(7)` J per hour