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

A 5 metre long wire is fixed to the ceiling. A weight of 10 kg is hung at the lower end and is 1 metre above the floor. The wire is elongated by 1 mm. The energy stored in the wire due to stretching is

1. Zero

2. 0.05 joule

3. 100 joule

4. 500 joule

Two soap bubbles of radii r₁ and r₂ equal to 4 cm and 5 cm are touching each other over a common surface S₁S₂ (shown in figure). Radius of common surface will be

1. 4 cm

2. 20 cm

3. 5 cm

4. 4.5 cm

Two capillaries made of same material but of different radii are dipped in a liquid. The rise of liquid in one capillary is 2.2 cm and that in the other is 6.6 cm. The ratio of their radii is

1. 9 : 1

2. 1 : 9

3. 3 : 1

4. 1 : 3

In a surface tension experiment with a capillary tube water rises upto 0.1 m. If the same experiment is repeated on an artificial satellite, which is revolving around the earth, water will rise in the capillary tube upto a height of

1. 0.1 m

2. 0.2 m

3. 0.98 m

4. Full length of the capillary tube

A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions. If T is the surface tension of soap solution, the energy spent in the blowing is

1. $3{\mathrm{\pi Tr}}^2$

2. $6{\mathrm{\pi Tr}}^2$

3. $12{\mathrm{\pi Tr}}^2$

4. $24{\mathrm{\pi Tr}}^2$