Mechanical Properties of Fluids

A wooden block is taken to the bottom of a deep, calm lake of water and then released. It rises up with a :

• constant acceleration

• decreasing aceleration

• constant velocity

• decreasing velocity

A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in the figure. Let V_A, V_B, V_C be the potentials at points A, B and C respectively. Then :

• V_C > V_B

• V_B > V_c

• V_A > V_B

• V_A = V_C

The radius R of the soap bubble is doubled under isothermal condition. If T be the surface tension of soap bubble, the required surface energy in doing so is given by:

• 32πR²T

• 24πR²T

• 8πR²T

• 4πR²T

Mercury boils at 367°C. However, mercury thermometers are made such that they can measure temperature upto 500°C. This is done by:

• maintaining vacuum above the mercury column in the stem of the thermometer

• filling nitrogen gas at high pressure above the mercury column

• filling oxygen gas at high pressure above the mercury column

• filling nitrogen gas at low pressure above the mercury column

An ice-cube of density 900 kg/m³ is floating in the water of density 1000 kg/m³ The percentage of volume of the ice-cube outside the water is:

• 20 %

• 35 %

• 10 %

• 25 %

A tank is filled with water upto height H. When a hole is made at a distance h below the level of water, what will be the horizontal range of water jet?

• 2√h(H - h)

• 4√h(H + h)

• 4√h(H - h)

• 2√h(H + h)

A raft of wood of mass 120 kg floats in water. The weight that can be put on the raft to make it just sink should be (draft = 600 kg/m³) :

• 80 kg

• 50 kg

• 60 kg

• 30 kg

Eight small drops, each of equal charges and radii are coalesce to form a big drop. The capacity of bigger drop in comparison to each smaller drop will be :

• 4 times

• 2 times

• 32 times

• 8 times

The surface tension of the soap solution is T. The work done in forming a soap bubble of radius r, is :

• $8{\mathrm{\pi r}}^2\mathrm{T}$

• $4{\mathrm{\pi r}}^2\mathrm{T}$

• $\frac{4}{3}{\mathrm{\pi r}}^2\mathrm{T}$

• $\frac{8}{3}{\mathrm{\pi r}}^2\mathrm{T}$

Given that the surface tension of water is 75 dyne/cm, its density 1 g/cc and angle of contact zero, the height to which water rises in a capillary tube of 1 mm diameter is (Take g = 10 m/s²)

• 9.0 cm

• 7.5 cm

• 6.0 cm

• 3.0 cm