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. $24{\mathrm{\pi Tr}}^2$

At which of the following temperatures, the values of surface tension of water is minimum

1. $4°\mathrm{C}$

2. $25°\mathrm{C}$

3. $50°\mathrm{C}$

4. $75°\mathrm{C}$

The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be 75 cm of Hg and the density of water to be 1/10 of the density of mercure, the depth of the lake is

1. 5 m

2. 10 m

3. 15 m

4. 20 m

A hemispherical bowl just floats without sinking in a liquid of density $1.2\times {10}^3<mspace\; width="1em"></mspace>\mathrm{kg}/{\mathrm{m}}^3$. If outer diameter and the density of the bowl are 1 m and $2\times {10}^4<mspace\; width="1em"></mspace>\mathrm{kg}/{\mathrm{m}}^3$ respecitvely, then the inner diameter of the bowl will be

1. 1.94 m

2. 1.97 m

3. 0.98 m

4. 1.99 m