HARD
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A uniform solid cylinder of length submerged partially in two immiscible liquids is in equilibrium as shown. If one-third length of the cylinder is submerged in liquid of density
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Important Questions on Mechanical Properties of Fluids
HARD
Two masses and are connected at the two ends of a massless rigid rod of length The rod is suspended by a thin wire of torsional constant at the centre of mass of the rod-mass system (see figure). Because of torsional constant the restoring torque is for angular displacement If the rod is rotated by and released, the tension in it when it passes through its mean position will be:
HARD
Two spheres and of equal radii have densities and , respectively. The spheres are connected by a massless string and placed in liquids and of densities and and viscosities and , respectively. They float in equilibrium with the sphere in and sphere in and the string being taut (see figure). If sphere alone in has terminal velocity and alone in has terminal velocity , then
MEDIUM
The time period of oscillation of a simple pendulum of length suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination , is given by :
HARD
Consider the wall of a dam to be straight with height and length . It holds a lake of water of height on one side. Let the density of water be Denote the torque about the axis along the bottom length of the wall by . Denote also a similar torque due to the water up to height and wall length by . Then, (ignore atmospheric pressure) is
HARD
A rectangular block of mass and area of cross-section floats in a liquid of density . If it is given a vertical displacement from equilibrium, it undergoes oscillation with a time period . Then
HARD
Air (density ) is being blown on a soap film (surface tension ) by a pipe of radius with its opening right next to the film. The film is deformed and a bubble detaches from the film when the shape of the deformed surface is a hemisphere. Given that the dynamic pressure on the film due to the air blown at speed is the speed at which the bubble formed is
MEDIUM
A car is moving on a plane inclined at to the horizontal with an acceleration of parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is (Take )
HARD
A block with mass is connected by a massless spring with stiffness constant to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude about an equilibrium position . Consider two cases : (i) when the block is at and (ii) when the block is at . In both the cases, a particle with mass is softly placed on the block after which they stick to each other. Which of the following statement(s) is(are) true about the motion after the mass is placed on the mass ?
MEDIUM
A cylindrical block of wood of mass and radius is floating in water with its axis vertical. When it is depressed a little and then released, it starts executing simple hormonic motion (SHM). The frequency of the SHM, executed by the block is:
(Assume and let is the density of the water)
EASY
The time period of a simple pendulum inside a stationary lift is . If the lift starts moving upwards with an acceleration of , its time period will be,
HARD
A bubble of radius in water of density is expanding uniformly at speed . Given that water is incompressible, the kinetic energy of water being pushed is
MEDIUM
Two light identical springs of spring constant are attached horizontally at the two ends of a uniform horizontal rod of length and mass The rod is pivoted at its center 'O' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is:
HARD
Consider the configuration of a stationary water tank of cross-section area and a small bucket as shown in figure below;
What should be the speed of the bucket, so that the water leaking out of a hole of cross-section area (as shown) from the water tank does not fall outside the bucket?
(Take, and ).
HARD
A very large block of ice of the size of a volleyball court and of uniform thickness of is floating on water. A person standing near its edge wishes to fetch a bucketful of water using a rope. The smallest length of rope required for this is about
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For a simple pendulum, a graph is plotted between its kinetic energy (K.E.) and potential energy (P.E.) against its displacement d. which one of the following represents these correctly? (graphs are schematic and not drawn to scale)
MEDIUM
A particle is executing simple harmonic motion of amplitude along the -axis, about When its potential Energy equals kinetic energy the position of the particle will be:
HARD
A particle executes simple harmonic motion with an amplitude of . When the particle is at from the mean position, the magnitude of its velocity in units is equal to that of its acceleration. Then, its periodic time in seconds is:
MEDIUM
What is the time period of the pendulum in a lift, which is falling freely under gravity
MEDIUM
A rod of mass and length is suspended at its middle by a wire. It exhibits torsional oscillations. If two masses, each of mass , are attached at a distance from its centre on both sides, it reduces the oscillation frequency by . The value of ratio is close to
HARD
A cylindrical plastic bottle of negligible mass is filled with of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency If the radius of the bottle is then is close to: density of water
