A body of density d₁ is counter poised by Mg of weights of density d₂ in air of density d. Then the true mass of the body is

(1) M

(2) $\mathrm{M}\left(1-\frac{\mathrm{d}}{{\mathrm{d}}_2}\right)$

(3) $M\left(1-\frac{d}{d_1}\right)$

(4) $\frac{M\left(1-\frac{d}{d_2}\right)}{\left(1-\frac{d}{d_1}\right)}$

A tank filled with water has two taps to exhaust and pour. A hollow spherical ball is half submerged in water. Through one tap, water is taken out and through another tap, a liquid of density double the density of water is poured in tank such that volume of liquid in tank remains constant. Sphere will

1. go down

2. go up

3. maintain same height

4. sink to bottom

Water is flowing continuously from a tap having an internal diameter 8 x 10^-3 m. The water velocity as it leaves the tap is 0.4 ms^-1. The diameter of the water stream at a distance 2 x 10^-1 m below the tap is close to

1. 5.0 x 10^-3 m

2. 7.5 x 10^-3 m

3. 9.6 x 10^-3 m

4. 3.6 x 10^-3 m

Two metal spheres are falling through a liquid of density $2\times {10}^3\mathrm{kg}/{\mathrm{m}}^3$ with the same uniform speed. The material density of sphere 1 and sphere 2 are $8\times {10}^3\mathrm{kg}/{\mathrm{m}}^3$ and $11\times {10}^3\mathrm{kg}/{\mathrm{m}}^3$ respectively. The ratio of their radii is

1. $\frac{11}{8}$

2. $\sqrt{\frac{11}{8}}$

3. $\frac{3}{2}$

4. $\sqrt{\frac{3}{2}}$

A long cylindrical glass vessel has a small hole of radius r at its bottom. The depth to which the vessel can be lowered vertically in a deep water bath without any water entering inside is (surface tension = T and d = density of water)

1. $\frac{4\mathrm{T}}{\text{ rdg }}$

2. $\frac{5\mathrm{T}}{\text{ rdg }}$

3. $\frac{3\mathrm{T}}{\text{ rdg }}$

4. $\frac{2\mathrm{T}}{\text{ rdg }}$

A candle of diameter d is floating on a liquid in a cylindrical container of diameter D (D>>d) as shown in figure. If it is buming 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 2cm/hour

4. go up the rate of 1 cm/hour

A ball of relative density 0.8 falls into water from a height of 2 m. The depth to which the ball will sink is (neglect viscous forces)

1. 8 m

2. 2 m

3. 6 m

4. 16 m

In the given figure, the velocity v₃ will be

1. 2 m/s

2. 4 m/s

3. 1 m/s

4. 3 m/s

There is hole of area a at the bottom of a cylindrical of area A. Water is filled upto a height h and water flows out in t second. If water is filled to a height 4h, it will flow out in time

1. $\frac{t}{4}$

2. 2t

3. 4t

4. $\frac{t}{2}$

There is a hole in the bottom of tank having water. If total pressure at bottom is 3 atm $(1 \mathrm{atm}={10}^5\mathrm{N}/{\mathrm{m}}^2)$ then the velocity of water flowing from hole is

1. $\sqrt{400} m/s$

2. $\sqrt{600} m/s$

3. $\sqrt{60} m/s$

4. None of these