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This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A bubble having surface tension T and radius R is formed on a ring of radius b `(b lt gt R)` . Air is blown inside the tube held in front of the ring , with velocity `upsilon` as shown in fig. The air molecules collides perpendicularly with the wall of the bubble and stops. Calculate the radius R at which the bubble and stops. Calculate the radius R at which the bubble separates from the ring. |
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Answer» Correct Answer - B::D KEY CONCEPT: When the force due to excess pressure in the bubble equals the force of air striking at the bubble, the bubble will detach from the ring. `:. rhoAv^2=(4T)/(R)xxAimpliesR=(4T)/(rhov^2)` |
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| 2. |
A uniform solid cylinder of density `0.8g//cm^3` floats in equilibrium in a combination of two non-mixing liquids A and B with its axis vertical. The densities of the liquids A and B are `0.7g//cm^3` and `1.2g//cm^3`, respectively. The height of liquid A is `h_A=1.2cm.` The length of the part of the cylinder immersed in liquid B is `h_B=0.8cm`. (a) Find the total force exerted by liquid A on the cylinder. (b) Find h, the length of the part of the cylinder in air. (c) The cylinder is depressed in such a way that its top surface is just below the upper surface of liquid A and is then released. Find the acceleration of the cylinder immediately after it is released. |
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Answer» Correct Answer - A::B::C (a) As the pressure exerted by liquid A on the cylinder is radial and symmetric, the force due to this pressure cancels out and the net value is zero. (b) For equilibrium, Buoyant force =weight of the body `impliesh_Arho_A Ag+h_Brho_BAg =(h_A+h+h_B)Arho_Cg` (where `rho_C=` density of cylinder) `h=((h_Arho_A+h_Brho_B)/(rho_C))-(h_A+h_B)=0.25cm` (c) `a=(F_(Buoyant-Mg)/(M))` `=[(h_Arho_A+rho_B(h+h_B)-(h+h_A+h_B)rho_C)/(rho_C(h+h_A+h_C))]g` `=g/6` upwards |
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| 3. |
A man is sitting in a boat which is floating in a pond. If the man drinks some water from the pond, the level of water in the pond decreases. |
| Answer» When the man drinks some water from the pond, his weight increases and therefore the boat will sink further. The further sinking of the boat will displace the same volume of water in pond as drunk by man. Therefore, there will no change in the level of water in the pond. | |
| 4. |
Water in a closed tube (see fig) is heated with one arm vertically placed above a lamp. Water will begin to circulate along the tube in counter-clockwise direction. |
| Answer» When water is heated at end A, the density decreases and the water moves up. This is compensated by the movement of water from B to A i.e., in clockwise direction. | |
| 5. |
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. (a) zeroB. (b) equal to the weight of the liquid displacedC. (c) equal to the weight of the body in airD. (d) equal to the weight of the immersed portion of the body |
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Answer» Correct Answer - A The whole system falls freely under gravity Upthrust = weight of fluid displaced =(mass of fluid displaced)xg For a freely falling body, `g=0` `:. Upthrust=0` |
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| 6. |
A wire fixed at the upper end stretches by length l by applying a force F. The work done in stretching isA. (a) 2FlB. (b) FlC. (c) `(F)/(2l)`D. (d) `(Fl)/(2)` |
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Answer» Correct Answer - D Work done by constant force in displacing the object by a distance l. `=1/2xxFo rcexxextension=(Fl)/(2)` |
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| 7. |
A homogeneous solid cylinder of length L(LltH/2), cross-sectional area A/5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L/4 in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure `P_0`. Then density D of solid is given by A. (a) `5/4d`B. (b) `4/5d`C. (c) `4d`D. (d) `d/5` |
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Answer» Correct Answer - A Weight of cylinder=Upthrust due to upper liquid+Upthrust due to lower liquid. `D(A/5xxLxxg)=d(A/5)(3/4L)g+2d(A/5)(L/4)xxg` `:.D=(5d)/(4)` |
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| 8. |
A block of ice with a lead shot embedded in it is floating on water contained in a vessel. The temperature of the system is maintained at `0^@C` as the ice melts. When the ice melts completely the level of water in the vessel rises. |
| Answer» When the block of ice melts, the lead shot will ultimately sink in the water. When lead shot sinks, it will displace water equal to its own volume. But when lead shot was embedded in ice, it displaced more volume of water than its own volume because `d_(l ead)gtd_(water)`. Therefore, level of water will fall. | |
| 9. |
A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?A. (a) B. (b) C. (c) D. (d) |
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Answer» Correct Answer - C In case of water, the meniscus shape is concave upwards. Also according to ascent formula `h=(2Tcostheta)/(rrhog)` The surface tension (T) of soap solution is less than water. Therefore rise of soap solution in the capillary tube is less as compared to water. As in the case of water, the meniscus shape of soap solution is also concave upwards. |
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| 10. |
Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, density of liquid is `rho` and L is its latent heat of vaporization.A. (a) `rhoL//T`B. (b) `sqrt(T//rhoL)`C. (c) `T//rhoL`D. (d) `2T//rhoL` |
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Answer» Correct Answer - D When radius is decrease by `DeltaR`, `4piR^2rhoL=4piT[R^2-(R-DeltaR)^2]` `impliesrhoR^2DeltaRL=T[R^2-R^2+2RDeltaR-DeltaR^2]` `impliesrhoR^2DeltaRL=T2RDeltaR` [`DeltaR` is very small] `implies R=(2T)/(rhoL)` |
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| 11. |
A cylindrical tank has a hole of diameter 2r in its bottom. The hole is covered wooden cylindrical block of diameter 4r, height h and density `rho//3`. Situation I: Initially, the tank is filled with water of density `rho` to a height such that the height of water above the top of the block is `h_1` (measured from the top of the block). Situation II: The water is removed from the tank to a height `h_2` (measured from the bottom of the block), as shown in the figure. The height `h_2` is smaller than h (height of the block) and thus the block is exposed to the atmosphere. In situation 2, if `h_2` is further decreased, thenA. (a) cylinder will not move up and remains at its original positionB. (b) for `h_2=h/3`, cylinder again starts moving upC. (c) for `h_2=h/4`, cylinder again starts moving upD. (d) for `h_2=h/5`, cylinder again starts moving up |
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Answer» Correct Answer - A When the height `h_2` of water level is further decreased, then the upward force acting on the wooden block decreases. The total force downward remains the same. This difference will be compensated by the normal reaction by the tank wall on the wooden block. Thus the block does not moves up and remains at its original position. |
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| 12. |
When temperature of a gas is `20^@C` and pressure is changed from `p_1=1.01xx10^5Pa` to `p_2=1.165xx10^5Pa` then the volume changed by `10%`. The bulk modulus isA. (a) `1.55xx10^5Pa`B. (b) `0.115xx10^5Pa`C. (c) `1.4xx10^5Pa`D. (d) `1.01xx10^5Pa` |
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Answer» Correct Answer - A `B=(Deltap)/(DeltaV//V)=((1.165xx10^5-1.01x10^5))/(0.1)=1.55xx10^5Pa` |
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| 13. |
A spring of force constant `800N//m` has an extension of 5cm. The work done in extending it from 5cm to 15cm isA. (a) 16JB. (b) 8JC. (c) 32JD. (d) 24J |
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Answer» Correct Answer - B Small amount of work done in extending the spring by `dx` is `dW=kxdx` `:. W=kint_(0.05)^(0.15)xdx=(800)/(2)[(0.15)^2-(0.05)^2]=8J` |
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| 14. |
If the terminal speed of a sphere of gold (density `=19.5kg//m^3`) is `0.2m//s` in a viscous liquid (density `=1.5kg//m^3`), find the terminal speed of a sphere of silver (density `=10.5kg//m^3`) of the same size in the same liquidA. (a) `0.4m//s`B. (b) `0.133m//s`C. (c) `0.1m//s`D. (d) `0.2m//s` |
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Answer» Correct Answer - C Terminal velocity, `v_T=(2r^2(d_1-d_2)g)/(9eta)` `(v_(T_2))/(0.2)=(10.5-1.5)/(19.5-1.5)impliesv_(T_2)=0.2xx9/18=0.1m//s` |
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| 15. |
One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end fo another horizontal thin copper wire of lenth L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire isA. (a) 0.25B. (b) 0.50C. (c) 2.00D. (d) 4.00 |
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Answer» Correct Answer - C `Y=(F//pi(2R)^2)/(Deltal_1//2L)=(F//piR^2)/(Deltal_2//L)` `:. (Deltal_2)/(Deltal_1)=2` |
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| 16. |
Work done in increasing the size of a soap bubble from a radius of 3cm to 5cm is nearly (Surface tension of soap solution `=0.03Nm^-1`)A. (a) `0.2pimJ`B. (b) `2pimJ`C. (c) `0.4pimJ`D. (d) `4pimJ` |
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Answer» Correct Answer - C W=Tx change in surface area `W=2T4pi[(5^2)-(3)^2]xx10^4` `=2xx0.03xx4pi[25-9]xx10^-4J=0.4pixx10^3J` `=0.4pimJ` |
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