The vessel shown in the figure has two sections of areas of cross–section A₁ and A₂. A liquid of density r fills both the sections, up to a height h in each. Neglect atmospheric pressure

A circular cylinder of radius R and height H is filled with water to a height H. It starts rotating about its axis with constantly increasing angular speed. Choose the correct alternatives

A Siphon tube is used to remove liquid from a container as shown in figure. In order to operate the Siphon tube it must initially be filled with the liquid

The velocity of the water flowing from the inlet pipe is less than the velocity of water flowing out from the spin pipe B.

A small hole is made at a height of h¢ = (1/) m from the bottom of a cylindrical water tank and at a depth of h = m from the upper level of water in the tank. The distance, where the water emerging from the hole strikes the ground is:

In the figure shown a liquid is flowing through a tube at the rate of 0.1 m³/sec. The tube is branched into two semi circular tubes of cross sectional area A/3 and 2A/3. The velocity of liquid at Q is (the cross-section of the main tube (A) = 10^-2 m² and V_P = 20 m/sec.):

In a hydraulic lift, used at a service station the radius of the large and small piston are in the ratio of 20 : 1. What weight placed on the small piston will be sufficient to lift a car of mass 1500kg?

A piston of a syringe pushes a liquid with a speed of 1 cm/sec. The radii of the syringe tube and the needle are R = 1cm and r = 0.5 mm respectively. The velocity of the liquid coming out of the needle is:

A cube of mass m and density D is suspended from the point P by a spring of stiffness k. The system is kept inside a beaker filled with a liquid of density d. The elongation in the spring, assuming D > d, is:

A particle of mass m (where m is the mass in gram) is released from point O with initial velocity zero. The work done by gravitational force on the particle, when it is taken from O to B, is

Gravitational potential at the centre of curvature of a hemispherical bowl of radius R and mass M is V.

Inside a uniform sphere of mass M and radius R, a cavity of radius R/3 is made in the sphere as shown

A, B, C are vertices of an equilateral triangle imagined in free space (no gravity). First a mass m is brought from infinity to point A and the work done in doing so is W_A. Then keeping m fixed at A, another identical mass m is brought from infinity to point B. The work done is W_B. The work done by the another identical mass m brought from infinity to C is W_C keeping A and B fixed. Then

The ratio of earth’s orbital angular momentum (about the sun) to its mass is 4.4 × 10¹⁵ m²/s. The area enclosed by earth’s orbit is approximately

The figure shows a uniform smooth solid cylinder A of radius 4 m rolling without slipping on the 8 kg plank which in turn is supported by a fixed smooth surface. Block B, is known to accelerate down with 6 m/s².
(Take g = 10 m/s²)

What is the angular acceleration of the cylinder ?

If the bisector of angle A of a DABC meets BC at D and AB=c,BC=a CA=b then D divides BC in the ratio…

For such questions, we should know about angle bisector properties. While taking ratio, we have to careful that we are taking ratio of adjacent sides.