Three tubes X, Y and Z are connected to a horizontal pipe in which ideal liquid is flowing. The radii of the tubes X, Y and Z at the junction are respectively 3 cm, 1 cm and3 cm. It can be said

the height of the liquid in the tube A is maximum.
the height of liquid in the tubes A and B is same.
the height liquid in the tubes A,B and C is same.
the height of the liquid in the tubes A and C is the same.

Solution

the height of the liquid in the tubes A and C is the same.

A fast train goes past way side station platform at high speed. A person standing at the edge of the platform is

attracted to train
repelled from train
unaffected by outgoing train
affected only if the train's speed is more than the speed of sound

Solution

Apply Bernoulli’s theorem.

A water tank of height 10m, completely filled with water is placed on a level ground. It has two holes one at 3 m and the other at 7 m from its base. The water ejecting from

both the holes will fall at the same spot
upper hole will fall farther than that from the lower hole
upper hole will fall closer than that from the lower hole
more information is required

Solution

The pressure energy per unit volume of a liquid is

^p⁄_ρ
p
p × ρ
^ρ⁄_p

Solution

Bernoulli’s theorem.

A beaker with a liquid of density 1.4 g cm^–3 is in balance over one pan of a weighing machine. If a solid of mass 10 g and density 8 g cm^–3 is now hung from the top of that pan with a thread and sinking fully in the liquid without touching the bottom, the extra weight to be put on the other pan for balance will be

10.0 g
8.25 g
11.75 g
–1.75 g

Solution

10g is the force on water = extra wt. on other pan.

Two vessels A and B of cross-sections as shown in figure contain a liquid up to the same height. As the temperature rises, the liquid pressure at the bottom (neglecting expansion of the vessels) will

increase in A, decrease in B
increase in B, decrease in A
increase in both A and B
decrease inboth A and B

Solution

As temperature rises, the density decreases, height in creases. In A, the top cross-section is smaller.Therefore h_A > h_B.

Figure here shows the vertical cross section of a vessel filled with a liquid of density ρ. The normal thrust per unit area on the walls of the vessel at the point P, as shown, will be

hρg
Hρg
(H – h) ρg
(H – h) ρg cosθ

Solution

Pressure is proportional to depth from the free surface and is same in all directions.

Figure shows a weigh-bridge, with a beaker P with water on one pan and a balancing weight R on the other. A solid ball Q is hanging with a thread outside water. It has volume 40cm³ and weighs 80 g. If this solid is lowered to sink fully in water, but not touching the beaker anywhere, the balancing weight R’ will be

same as R
40 g less than R
40 g more than R
80 g more than R

Solution

Upthrust = weight of 40 cm³ of water

= 40 g = down thrust on water

Two pieces of metals are suspended from the arms of a balance and are found to be in equilibrium when kept immersed in water. The mass of one piece is 32 g and its density 8 g cm^-3. The density of the other is 5 g per cm3.Then the mass of the other is

28 g
35 g
21 g
33.6 g

Solution

Volume of first piece of metal = ³²⁄₈ = 4 cm³

Upthrust = 4 gf

Effective weight = (32 – 4) gf = 28 gf

If m be the mass of second body,volume of second

body is ^m⁄₅

Now 28 = m - ^m⁄₅ ⇒ m = 35 g

An egg when placed in ordinary water sinks but floats when placed in brine. This is because

density of brine is less than that of ordinary water
density of brine is equal to that of ordinary water
density of brine is greater than that of ordinary water
None of these

Solution

Brine due to its high density exerts an upthrust which can balance the weight of the egg.

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