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A balloon with mass m is descending down with an acceleration a (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration a?
1. $\frac{2\mathrm{ma}}{\mathrm{g}<mspace\; width="1em"></mspace>+\hspace{0.17em}\mathrm{a}}$
2. $\frac{2\mathrm{ma}}{\mathrm{g}<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>\mathrm{a}}$
3. $\frac{\mathrm{ma}}{\mathrm{g}<mspace\; width="1em"></mspace>+\hspace{0.17em}\mathrm{a}}$
4. $\frac{\mathrm{ma}}{\mathrm{g}<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>\mathrm{a}}$

The excess pressure inside a spherical drop of water is frour times that of another drop. Then their respective mass ratio is :
1. 1 : 16
2. 8 : 1
3. 1 : 4
4. 1 : 64

A liquid X of density 3.36 g ${\mathrm{cm}}^{-3}$ is poured in the right arm of a U-tube, which contains Hg. Another liquid Y is poured in the left arm with a height of 8 cm. Upper levels of X and Y are the same. What is the density of Y?

1. 0.8 ${\mathrm{gcc}}^{-1}$
2. 1.2 ${\mathrm{gcc}}^{-1}$
3. 1.4 ${\mathrm{gcc}}^{-1}$
4. 1.6 ${\mathrm{gcc}}^{-1}$

A wooden ball of density D is immersed in water of density d to a depth h below the surface of the water and then released. Up to what height will the ball jump out of water?
1. $\frac{\mathrm{d}}{\mathrm{D}}h$
2. $\left(\frac{\mathrm{d}}{\mathrm{D}}<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>1\right)h$
3. $h$
4. Zero

A piece of solid weighs 120 g in air, 80 g in water and 60 g in a liquid. The relative density of the solid and that of the liquid are respectively :
1. 3, 2
2. 2,$\frac{3}{4}$
3. $\frac{3}{2}$, 2
4. 3, $\frac{3}{2}$

A solid sphere of volume V and density ρ floats at the interface of two immiscible liquids of densities ρ${}_1$ and ρ${}_2$ respectively. If ρ${}_1$ < ρ < ρ${}_2$, then the ratio of the volume of the parts of the sphere in upper and lower liquids is :
1. $\frac{{\mathrm{\rho }}_2-\mathrm{\rho }}{\mathrm{\rho }-{\mathrm{\rho }}_1}$
2. $\frac{\mathrm{\rho }<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>{\mathrm{\rho }}_1}{\mathrm{\rho }<mspace\; width="1em"></mspace>+\hspace{0.17em}{\mathrm{\rho }}_2}$
3. $\frac{\mathrm{\rho }<mspace\; width="1em"></mspace>+\hspace{0.17em}{\mathrm{\rho }}_2}{\mathrm{\rho }<mspace\; width="1em"></mspace>+\hspace{0.17em}{\mathrm{\rho }}_1}$
4. $\frac{\sqrt{{\mathrm{\rho }}_1<mspace\; width="1em"></mspace>{\mathrm{\rho }}_2}}{\mathrm{\rho }}$

A wooden block, with a coin placed on its top, floats in water as shown in the figure. The distances h and l are shown there. After some time, the coin falls into the water, then :

1. Both l and h increase
2. Both l and h decrease
3. l decreases and h increases
4. l increases and h decreases

A small spherical ball falling through a viscous medium of negligible density has terminal velocity v. Another ball of the same mass but of radius twice that of the earlier one falling through the same viscous medium will have a terminal velocity :
1. v
2. $\frac{\mathrm{v}}{4}$
3. $\frac{\mathrm{v}}{2}$
4. 4v

A mercury drop of radius 1.0 cm is sprayed into 10${}^6$ droplets of equal sizes. The energy expended in this process is : (surface tension of mercury is equal to 32 × 10${}^{-2}$ Nm${}^{-1}$)
1. 3.98 x 10${}^{-4}$ J
2. 8.46 x 10${}^{-4}$ J
3. 3.98 x 10${}^{-2}$ J
4. 8.46 x 10${}^{-2}$ J

Water is flowing through a channel (lying in a vertical plane) as shown in the figure. Three sections A, B, and C are shown. Sections B and C have an equal area of cross-section. If P_A, P_B, and P_C are the pressures at A, B, and C respectively, then-

1. ${\mathrm{P}}_{\mathrm{A}}>{\mathrm{P}}_{\mathrm{B}}={\mathrm{P}}_{\mathrm{C}}$
2. ${\mathrm{P}}_{\mathrm{A}}<{\mathrm{P}}_{\mathrm{B}}<{\mathrm{P}}_{\mathrm{C}}$
3. ${\mathrm{P}}_{\mathrm{A}}<{\mathrm{P}}_{\mathrm{B}}={\mathrm{P}}_{\mathrm{C}}$
4. ${\mathrm{P}}_{\mathrm{A}}>{\mathrm{P}}_{\mathrm{B}}>{\mathrm{P}}_{\mathrm{C}}$