A 10cm long wire is placed horizontally on the surface of water and is gently pulled up with a force of $2\times {10}^{-2}N$ to keep the wire in equilibrium. The surface tension, in $N{m}^{-1}$ of water is

1. 0.1

2. 0.2

3. 0.001

4. 0.002

The mean density of sea water is $\mathrm{\rho }$ and Bulk modulus is B. The change in density of sea water in going from the surface of water to depth h is :-

(1) $\frac{\mathrm{\rho gh}}{\mathrm{B}}$

(2) B$\mathrm{\rho }$gh

(3) $\frac{{\mathrm{\rho }}^2\mathrm{gh}}{\mathrm{B}}$

(4) $\frac{{\mathrm{B\rho }}^2}{\mathrm{gh}}$

A thin wire is bent in the form of a ring of diameter 3.0 cm. The ring is placed horizontally on the surface of soap solution and then raised up slowly upwarc force necessary to break the vertical film formed between the ring and solution is :-

1. 6$\mathrm{\pi }$T Dyne

2. 2$\mathrm{\pi }$T dyne

3. 4$\mathrm{\pi }$T dyne

4. 3$\mathrm{\pi }$T dyne

An L-shaped tube with a small orifice is held in a water stream as shown in figure. The upper end of the tube is 10.6 cm above the surface of water. What will be the height nearly of the jet of water coming from the orifice? Velocity of water stream is 2.45 m/s

1. zero

2. 20.0 cm

3. 10.6 cm

4. 40.0 cm

A candle of diameter d cm is floating on a liquid in a cylindrical container of diameter D (D>>d) as shown in figure. If it is burning at the rate of 2 cm/hour then the top of the candle will

1. remain at the same height

2. fall at the rate of 1 cm/hour

3. fall at the rate of 2 cm/hour

4. go up at the rate of 1 cm/hour

A hole is there in the bottom of the tank having water. If total pressure at bottom is 3 atm $(1<mspace\; width="1em"></mspace>\mathrm{atm}={10}^5<mspace\; width="1em"></mspace>\mathrm{N}<mspace\; width="1em"></mspace>{\mathrm{m}}^{-2})$

1. $\sqrt{400}<mspace\; width="1em"></mspace>{\mathrm{ms}}^{-1}$

2. $\sqrt{600}<mspace\; width="1em"></mspace>{\mathrm{ms}}^{-1}$

3. $\sqrt{60}<mspace\; width="1em"></mspace>{\mathrm{ms}}^{-1}$

4. None of these

The terminal speed attained by an aluminium sphere of radius 1 mm falling through water at $20°\mathrm{C}$ will be close to (Assume laminar flow, specific gravity of Al=2.7 and ${\mathrm{\eta }}_{\mathrm{water}}=8\times {10}^{-4}<mspace\; width="1em"></mspace>\mathrm{Pl}.$)

1. 9.2 m/s

2. 6.9 m/s

3. 4.6 m/s

4. 2.3 m/s

The total area of wings of an aeroplane is 10 m². The speed of air above and below the wings is 140 m/s and 110 m/s. Then the force on the aeroplane by air is? $\left({\mathrm{\rho }}_{\mathrm{A}}=1.28\frac{\mathrm{Kg}}{{\mathrm{m}}^3}\right)$

1. 48750 N

2. 48000 N

3. 95000 N

4. 50000 N

If x longitudinal strain is produced in a wire of Young's modulus Y, then energy stored in the material of the wire per unit volume is

1. ${\mathrm{Yx}}^2$

2. $2{\mathrm{Yx}}^2$

3. $\frac{1}{2}{\mathrm{Y}}^2\mathrm{x}$

4. $\frac{1}{2}{\mathrm{Yx}}^2$

A weight of 200 kg is suspended by vertical wire of length 600.5 cm. The area of cross-section of wire is 1 mm² by 0.5 cm. The Young's modulus of the material of wire will be

1. $2.35\times {10}^{12}<mspace\; width="1em"></mspace>\mathrm{N}/{\mathrm{m}}^2$

2. $1.35\times {10}^{10}<mspace\; width="1em"></mspace>\mathrm{N}/{\mathrm{m}}^2$

3. $13.5\times {10}^{11}<mspace\; width="1em"></mspace>\mathrm{N}/{\mathrm{m}}^2$

4. $23.5\times {10}^9<mspace\; width="1em"></mspace>\mathrm{N}/{\mathrm{m}}^2$