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51.

A light metal stick of square cross-section `(5cmxx5cm)` and length 4m mass 2.5 kg ad is shown in the figure below determine its angle of inclination when the water surface is 1m above the hinge. What minimum depth of water above high will be required to bring the metal stick in vertical position.

Answer» Correct Answer - `theta=30^(@)` depth of water `ge2m`
52.

A tube of uniform cross-section has two vertical portions connected with a horizontal thin tube 8 cm long at their lower ends. Enough water to occupy 22 cm of the tube is poured into one branch enough and enough oil o specific gravity 0.8 to occupy 22 cm is poured into the other find the position of the common surface E of the two liquids.

Answer» Correct Answer - `BE=6cm`
53.

The container shown below holds kerosene and air as indicated compute the pressure at P,Q,R and S in `KN//m^(2)` take spacific gravity of kerosene as 0.8

Answer» Correct Answer - `P_(p)=124.9kN//m^(2),P_(Q)=89.5kN//m^(2),P_(R)=89.5kN//m^(2),P_(S)=46.4kN//m^(2)`
54.

Two `U-`tube manometers are connected to a same tube as shown in figure. Datermine difference of pressure between `X` and `Y`. Take specific gravity of mercury as `13.6. (g = 10 m//s^(2), rho_(Hg) = 13600 kg//m^(3))`

Answer» Correct Answer - `248kN//m^(2)`
55.

A uniform rod of length b capable of tuning about its end which is out of water, rests inclined to the vertical. If its specific gravity is 5/9, find the length immersed in water.

Answer» Correct Answer - `(b)/(3)`
56.

Match the following `|{:(,"Table-1",,"Table-2"),((A),"stress"xx"Strain",(P),J),((B),(YA)/l,(Q),N//m),((C),Yl^(3),(R),J//m^(3)),((D),(Fl)/(AY),(S),m):}|`A. `{:(A,B,C,D),(r,q,p,s):}`B. `{:(A,B,C,D),(q,r,p,s):}`C. `{:(A,B,C,D),(p,r,r,q):}`D. `{:(A,B,C,D),(q,r,s,p):}`

Answer» Correct Answer - a
(a) (a) Stress `xx` Strain`=Nm^(-2)=Nm^(-2)*(m^(3))/(m^(3))=Jm^(-3)`
(b) `(YA)/(l)=(Nm^(-2)m^(2))/(m)=Nm^(-1)`
(c) `Yl^(3)=Nm^(-2)m^(3)=Nm=J`
(d) `(Fl)/(AY)=(Nm)/(m^(2)Nm^(-2))=m`
57.

Relation between `Y,etaandK is `A. `(y)/(3)=(3)/(k)+(1)/(eta)`B. `(9)/(y)=(eta)/(3)+(1)/(k)`C. `(3)/(y)=(1)/(eta)+(1)/(3k)`D. `(y)/(3)=(3)/(eta)+(1)/(k)`

Answer» Correct Answer - C
58.

Assertion: Every wire is like a spring, whose spring constant ,`K prop 1/l`, where l is length of wire. Reason : It follows from the relation `K = (YA)/(l)`A. (a) If both Assertion and Reason are true and the Reason is correctn explanation of the Assertion.B. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.C. If Assertion is true, but the Reason is false.D. If Assertion is false but the Reason is true.

Answer» Correct Answer - A
59.

A particle of mass `m` is under the influence of a force F which varies with the displacement x according to the relation `F=-kx +F_(0)` in which k and `F_(0)` are constants. The particle when disturbed will oscillateA. about x = 0, with `omega ne sqrt(k//m)`B. about x=0, with `omega = sqrt(k//m)`C. about `x=F_(0)//k` with `omega = sqrt(k//m)`D. about `x=F_(0)//k` with `omega ne sqrt(k//m)`

Answer» Correct Answer - C
60.

Which of the following relation is true ?A. `Y = 2 eta (1 - 2 sigma)`B. `Y = 2 eta (1 + 2 sigma)`C. `Y = 2 eta (1 - sigma)`D. `(1 + sigma) 2 eta = Y`

Answer» Correct Answer - d
We know that that `Y = (1 + sigma) 2 eta`
61.

A stretched rubber hasA. Increased kinetic energyB. Increased potential energyC. Decreased kinetic energyD. Decreased potential energy

Answer» Correct Answer - B
62.

Four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as followsA. L = 100 cm, r = 1 mmB. L = 200 cm, r = 3 mmC. L = 300 cm, r = 3 mmD. L = 400 cm, r = 4 mm

Answer» Correct Answer - a
`Delta L = (FL)/(AY)`
Because, wires of the same material are stretched by the same load. So, F and Y will be constant
`:. Delta L prop (L)/(pi r^(2))`
`:. Delta L_(1) = (100)/(pi xx (1 xx 10^(-3))^(2)) = (100)/(pi xx 10^(-6)) = (100)/(pi) xx 10^(-6)`
`:. Delta L_(2) = (200)/(pi xx (3 xx 10^(-3))^(2)) = (200)/(pi xx 9 xx 10^(-6)) = (22.2)/(pi) xx 10^(6)`
`:. Delta L_(3) = (300)/(pi xx (3 xx 10^(-3))^(2)) = (300)/(pi xx 9 xx 10^(-6)) = (33.3)/(pi) xx 10^(6)`
`:. Delta L_(4) = (400)/(pi xx (4 xx 10^(-3))^(2)) = (400)/(pi xx 16 xx 10^(-6)) = (25)/(pi) xx 10^(6)`
We can see that, L = 100 cm and r = 1 mm will elongate most.
63.

When load of 5 kg is hung on a wire than extension of 3 m takes place, then work done will beA. 75 jouleB. 60 jouleC. 50 jouleD. 100 joule

Answer» Correct Answer - A
64.

When a load of 10 kg is hung from the wire, then extension of 2m is produced. Then work done by restoring force isA. 200 JB. 100 JC. 50 JD. 25 J

Answer» Correct Answer - B
(b) `W=(1)/(2)` (Maximum stretching force)`xx`(Elongation produced)
`=(1)/(2)F Delta l`
Here, `F=mg=10xx10`
`Deltal=2m`
`therefore W=(1)/(2)(10xx10)xx2=100J`
65.

A wire suspended vertically from one of itsends is strached by attached a weight of `200 N` to the lower end . The weight streches the wire by `1 mm` . Then the elastic energy stored in the wire isA. 0.1 JB. 0.2 JC. 10 JD. 20 J

Answer» Correct Answer - B
(b) Energy stored by the spring
`U=(F^(2))/(2k)=(T^(2))/(2k)`
66.

The force constant of a wire is k and that of another wire is . 2k When both the wires are stretched through same distance, then the work doneA. `W_(2)=0.5 W_(1)`B. `W_(2)=W_(1)`C. `W_(2)=2W_(1)`D. `W_(2)=2W_(1)^(2)`

Answer» Correct Answer - C
`(W_(2))/(W_(1))=((1)/(2)k_(2)x^(2))/((1)/(2)k_(1)x^(2))`
`=(k_(2))/(k_(1))=(2k)/(k)`
`(W_(2))/(W_(1))=2 " " therefore W_(2)=2W_(1)`.
67.

A wire is stretched by `2xx10^(-2)`m due to the force of 10 N. Then the amount of work done to stretch the wire to a displacement of `4xx10^(-2)`m isA. 0.04 JB. 0.4 JC. 40 JD. 400 J

Answer» Correct Answer - B
`W_(1) =(1)/(2) Fl=(1)/(2)xx10 xx 2 xx 10^(-2) =0.1J`
`(W_(2))/(W_(1))=((l_(2))/(l_(1)))^(2)=((4xx10^(-2))/(2xx10^(-2)))^(2)=4`
`W_(2)=4W_(1)`
`=4xx0.1=0.4J`.
68.

The work done to stretch a wire through `1xx10^(-3)m` is 2J. Then the work done to stretch another wire of same material having half length and double the area of the cross section by `1xx10^(-3)m` is,A. `1//4` JB. 4 JC. 8 JD. 16 J

Answer» Correct Answer - C
`(W_(2))/(W_(1))=(F_(2)l_(2))/(F_(1)l_(1))=(2xx2)/(1xx1)`
`therefore W_(2)=W_(1) xx 4=4xx2=8J`.
69.

A wire is of lengths `l_(1)` and `l_(2)` when stretched by a force 4 N and 5 N respectively. Then the length of the wire when stretched by a force 7 N will beA. `3l_(2)-2l_(1)`B. `2l_(1)-3l_(2)`C. `7l_(1)-5l_(2)`D. `5l_(1)-9l_(2)`

Answer» Correct Answer - A
For first and second tension,
`L=(T_(2)l_(1)-T_(1)l_(2))/(T_(2)-T_(1))=(5l_(1)-4l_(2))/(5-4)`
`=5l_(1)-4l_(2) " " ` …(i)
For first and third tension,
`L=(T_(3)l_(2)-T_(1)l_(3))/(T_(3)-T_(1))=(7l_(1)-4l_(3))/(7-4)`
`=(7l_(1)-4l_(3))/(3) " " ` ...(ii)
From equation (I) and (ii),
`5l_(1)-4l_(2)=(7l_(1)-4l_(3))/(3)`
`15l_(1)-12l_(2)=7l_(1)-4l_(3)`
`8l_(1)-12l_(2)=-4l_(3)`
`3l_(2)-2l_(1)=l_(3).`
70.

With the data of the above problem, the strain energy per unit volume stored in the wires is,A. `4xx10^(2)J//m^(3)`B. `4 xx 10^(3)J//m^(3)`C. `4 J//m^(3)`D. `4xx10^(5)J//m^(3)`

Answer» Correct Answer - D
`u=(W)/(v) =(0.4)/(AL)=(0.4)/(10^(-6) xx1)`
`u=0.4xx10^(6)`
`=4xx10^(5) J//m^(3)`.
71.

A metal rod of length 2.5m and area of cross-section `2.5xx10^(-4)m^(2)` is elongated by `2.5xx10^(-3)`m by a force of 600N. Then energy stored in the rod is,A. 75 JB. 0.75 JC. 25 JD. 50 J

Answer» Correct Answer - B
`W=(1)/(2)Fl`
`=(1)/(2) xx 600 xx 2.5xx10^(-3)=0.75J`.
72.

A wire of diameter `1mm` breaks under a tension of 1000 N. Another wire, of same material as that of the first one, but of diameter `2mm` breaks under a tension ofA. 500 NB. 1000 NC. 10000 ND. 4000 N

Answer» Correct Answer - D
73.

A wire `(Y=1xx10^(11)N//m)` has length 1m and area `1mm^(2)`. The work required to increase its length by 2mm isA. `5xx10^(-2)J`B. `5xx10^(-3)J`C. `5xx10^(-4)J `D. `5xx10^(-5)J`

Answer» Correct Answer - A
`W=(1)/(2) (yAl^(2))/(L)`
`=(1)/(2) xx (2xx10^(11) xx 10^(-4) xx10^(-8))/(2) =0.5 xx 10^(-1)`
`=5 xx 10^(-2)J`
74.

A wire `(Y=1xx10^(11)N//m)` has length 1m and area `1mm^(2)`. The work required to increase its length by 2mm isA. 0.4 JB. 0.8 JC. 4 JD. 400 J

Answer» Correct Answer - A
`W=(1)/(2)F l=(1)/(2) xx (Al^(2))/(L)`
`=(1)/(2) xx (2xx10^(11) xx 10^(-6) xx 4 xx 10^(-6))/(1) =0.4J`.
75.

A wire of length `2m` is made from `10 cm^(2)` of copper. A force F is applied so that its length increases by `2mm`. Another wire of length `8m` is made from the same volume of copper. If the force F is applied to it, its length will increase byA. 0.8 cmB. 1.6 cmC. 2.4 cmD. 3.2 cm

Answer» Correct Answer - D
76.

A 1 m long steel wire of cross-sectional area `1 mm^(2)` is extended 1 mm. If `Y = 2 xx 10^(11) Nm^(-2)`, then the work done isA. 0.1 JB. 0.2 JC. 0.3 JD. 0.4 J

Answer» Correct Answer - a
Work done, `W = (1)/(2) Y (A)/(L) (Delta L)^(2)`
Given, `A = 1 mm^(2) = 10^(-6) m`,
`I = 1mm = 10^(-3) m Y = 2 xx 10^(11) Nm^(-2), L = 1m`
`:. W = (1)/(2) xx 2 xx 10^(11) xx 10^(-6) xx (10^(-3))^(2) = 0.1 J`
77.

A wire of length `50 cm` and cross sectional area of 1 sq. mm is extended by `1mm`. The required work will be `(Y=2xx10^(10) Nm^(-2))`A. `6xx10^(-2) J`B. `4xx10^(-2) J`C. `2xx10^(-2) J`D. `1 xx10^(-2) J`

Answer» Correct Answer - C
(c) Required work `W=(Yal^(2))/(2L)`
`=(2xx10^(10)xx10^(-6)xx(10^(-3))^(2))/(2xx50xx10^(-2))`
`=2xx10^(-2) J`
78.

Four identical rods are stretched by same force. Maximum extension is produced inA. L = 10 cm,D = 1 mmB. L = 100 cm,D = 2 mmC. L = 200cm,D=3 mmD. L = 300 cm,D=4 mm

Answer» Correct Answer - B
79.

Volume elasticity is possessed byA. solids onlyB. liquids onlyC. gases onlyD. all of the three states of matter

Answer» Correct Answer - D
80.

The isotermal elasticity of a gas is equal toA. DensityB. VolumeC. PressureD. Specific heat

Answer» Correct Answer - C
81.

The adiabatic elasticity of a gas is equal toA. `gamma xx` densityB. `gamma xx` volumeC. `gamma xx` pressureD. `gamma xx` specific heat

Answer» Correct Answer - C
82.

Statement-1: An ice cube is floating in water in a vessel at `0^(@)C` when ice cube melts level of water in the vessel remain same. Statement-2: Volume of melted ice is same as volume of water displaced by ice.A. Statement-1, is true, Statement-2 is true, Statement-2 is correct explanation for statement-1B. Statement-1 is true, statement-2 is true, statement-2 is NOT a correct explantion for statement-1C. statement-1 is true, statement-2 is falseD. statement-1 is false statement-2 is true

Answer» Correct Answer - A
83.

A paper disc of radius R from which a hole of radius r is cut out, is floating in a liquid of surface tension, T. What will be force on the disc due to surface tension?

Answer» `T=(F)/(L)=(F)/(L)=(F)/(2pi(R+r))thereforeF=2pi(R+r)T`
84.

Which statement is true for a metalA. `Y lt eta`B. `Y = eta`C. `Y gt eta`D. `Y lt 1//eta`

Answer» Correct Answer - C
85.

A light rod is supported horizontally by two wires of the same length L and area of cross -section A but of different moduli of elasticity `Y_(1)andY_(2)` A heavy mass m is suspended at a disance `a_(1)` from the first wire and `a_(2)` from the second wires Find the period of errtical oscillations of the mass.

Answer» Correct Answer - `2pi sqrt((m(a_(2)^(2)Y_(2)+a_(1)^(2)Y_(1)))/((a_(1)+a_(2))^(2)Y_(1)Y_(2))(L)/(A))`
86.

Statement-1: Two identical conincal pipes shown in figure have a drop of water. The water drop tens to move towards tapered end. Statement-2: Excess pressure is directed towards centre of curvature and inversely proportional to radius of curvature. Net excess pressure is therefore, directed towards tapered end. So the water drop tends to move towards tapered end. A. Statement-1, is true, Statement-2 is true, Statement-2 is correct explanation for statement-1B. Statement-1 is true, statement-2 is true, statement-2 is NOT a correct explantion for statement-1C. statement-1 is true, statement-2 is falseD. statement-1 is false statement-2 is true

Answer» Correct Answer - A
87.

The human ciculatory system can be thought of as a closed system of interconnecting pipes through which fluid is continuously circulated by two pumps the two pumps the right and left verticles of the heart, work as simple two-stroke force pumps. The muscles of the heart regulate the force by contracting and relaxing. the contraction (systole) lasts about 0.2s and a complete systole/diastole (contraction/relaxation) cycle lasts about 0.8s. For flood pressures and speeds in the normal range. the volume flow rate of blood through a blood vessel is directly proportional tot he pressure difference over a length of the vessel and to the fourth power of the radius of the vessel. The total mechanical energy per unit volume of blood just as it leaves the heart is `E//V=rhogh+P+rhov^(2)` Q. During intense exercise the volume of blood pumped per second by an athlete,s heart increases by a factor of 7, and his blood pressure increases by 20%/by what factor does the power output of the heart increase during exercise?A. 1.2B. 3.5C. 7D. 8.4

Answer» Correct Answer - D
88.

An object of weight W has a uniform rectangular cross section of a x2a and density of `0.25g//cm^(3)` part of it is immersed in water and the rectangle is tilted by `45^(underset(-)(@))` while one of its corners is just at the water surface find the torque of the buoyancy force to the centre of mass of the object.A. `2sqrt(2)aW`B. `(aW)/(sqrt(2))`C. `(aW)/(sqrt(2))`D. `(aW)/(2sqrt(2))`

Answer» Correct Answer - D
89.

A body of volume 100 c.c. is immersed completely in waer contained in a jar. The weight of water and the jar before immersion of the body was 700g wt. after immersion weight of water and jar will beA. 700 g wtB. 800 g wt.C. 500 g wtD. 100 g wt

Answer» Correct Answer - B
90.

A body floats in a liquid contained in a beaker. The whole system as shown in Figure falls freely under gravity. The upthrust on the body is A. zeroB. equal to weight of liquid displacedC. equal to weight of the body in airD. equal to the weight of the immersed body.

Answer» Correct Answer - A
91.

Water contained in a tank flows through an orifice of a diameter 2 cm under a constant pressure difference of 10 cm of water column. The rate of flow of water through the orifice isA. 44cc/sB. 4.4cc/sC. 444cc/sD. 4400cc/s

Answer» Correct Answer - C
92.

The diagram (figure) shows a venturimeter, through which water is flowing the speed of water at X is 2cm/s. the speed of water at Y (taking `g=1000cm//s^(2)`) isA. 23 cm/sB. 32 cm/sC. 101 cm/sD. 1024 cm/s

Answer» Correct Answer - B
93.

Statement-1: hot soup tastes better than the cold soup. Statement-2: Hot soup spread properly on our tondue due to lower surface tension.A. Statement-1, is true, Statement-2 is true, Statement-2 is correct explanation for statement-1B. Statement-1 is true, statement-2 is true, statement-2 is NOT a correct explantion for statement-1C. statement-1 is true, statement-2 is falseD. statement-1 is false statement-2 is true

Answer» Correct Answer - A
94.

A wooden block of volume `1000cm^(3)` is suspended from a spring balance its weight is 12 N in air. It is suspended in water such that half of the block is below the surface of water. The reading of spring balance isA. 10 NB. 9NC. 8 ND. 7 N

Answer» Correct Answer - D
95.

A bob of mass `10 kg` is attached to a wire `0.3 m` long. Its breaking stress is `4.8xx10^(7) N//m^(2)`. Then area of cross-section of the wire is `10^(-6) m^(2)`. What is the maximum angular velocity with which it can be rotated in a horizontal circle?A. `8 rad//s`B. `4 rad//s`C. `2 rad//s`D. `1rad//s`

Answer» Correct Answer - B
`T =mlomega^(2)`
` T/A = sigma_(max) = (mlomega^(2))/A`
:. ` omega = sqrt((sigma_(max)A)/(ml)`
`=sqrt((4.8xx10^(7)xx10^(-6))/(10xx10.3)`
`= 4 rad//s`
96.

The spring balance does not read properly after its long use becauseA. The elasticity of spring increasesB. The elasticity decreasesC. Its plastic power decreasesD. Its plastic power increases

Answer» Correct Answer - B
97.

Two wires of equal length are made of the same material. Wire A has a diameter that is twice as that of wire B. If identical weights are suspended from the ends of these wires, the increase in length isA. Four times for wire A as for wire BB. Twice for wire A as for white BC. Half for wire A as for wire BD. One-fourth for wire A as for wire B

Answer» Correct Answer - D
98.

The diagram shows a forc-extension graph for a rubber band. Consider of the following statements I. It will be easier to compress this rubber than expand it II. Rubber does not return to its original length after it is streched III. The rubber band will get heated id it is streched and realeased Which of these can be deduced from the graphA. only IIIB. II and IIIC. I and IIID. only I

Answer» Correct Answer - A
(a) Energy loss `prop` area of hysteris loop
Energy loss appear as heat
99.

The diagram shows a force extension graph for a rubber band, consider the following statements (I). It will be easier to compress this rubber than expand it. (II). Rubber does not return to its original length after it is stretched. (III). The rubber band will get heated if it is stretched and released. Which of these can deduced from the graph- (a). III only (b). II and III (c). I and III (d). I onlyA. III onlyB. II and IIIC. I and IIID. I only

Answer» Correct Answer - A
100.

A 5 metre long wire is fixed to the ceiling. A weight of `10kg` is hung at the lower end and is `1metre` above the floor. The wire was elongated by `1mm`. The energy stored in the wire duw to streching isA. 0.01JB. 0.05 JC. 0.02 JD. 0.04J

Answer» Correct Answer - B
(b) The energy stored in the wire.
`U=(1)/(2) xx F xx l=(1)/(2)mgl=(1)/(2)xx10xx10xx1xx10^(-3)=0.05 J`