Q#20
Which of the following graphs may represent the relationship between the capillary rise h and the radius r of the capillary?
Answer: (c)
The capillary rise h is inversely proportional to the radius of the capillary r. It means when r → 0, h → ∞ and when r → ∞, h → 0. This condition is best represented by the graph (c).
Q#21
Water rises in a vertical capillary tube up to a length of 10 cm. If the tube is inclined at 45°, the length of water risen in the tube will be
(a) 10 cm
(b) 10√2 cm
(c) 10/√2 cm
(d) none of these
Answer: (b)
When the tube is inclined, the vertical rise remains the same. So the water in the inclined tube rises to 10 sec45° = 10√2 cm.
Q#22
A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator, the length of the water column in the capillary tube will be
(a) 8 cm
(b) 6 cm
(c) 10 cm
(d) 20 cm.
Answer: (d)
The rise in a capillary tube is given as
h = 2Scosθ/rρg
When the entire arrangement is in a freely falling elevator, the effective g = 0. So the water will rise in the capillary up to its full length where at the top the meniscus will be convex upward. The condition is somewhat similar to a case when the length of the tube is smaller than the rise.
Q#23
Viscosity is a property of
(a) liquids only
(b) solids only
(c) solids and liquids only
(d) liquids and gases only.
Answer: (d)
Viscosity comes into play when something starts to flow. Since only liquids and gasses can flow it is their property.
Q#24
The force of viscosity is
(a) electromagnetic
(b) gravitational
(c) nuclear
(d) weak
Answer: (a)
The force of viscosity is due to the contact of the molecules like in friction. So it is an electromagnetic force.
Q#25
The viscous force acting between two layers of a liquid is given by F/A = η.dv/dz. This F/A may be called
(a) pressure
(b) longitudinal stress
(c) tangential stress
(d) volume stress
Answer: (c)
The force of viscosity acts between layers of the liquid and it acts along the surface. Thus F/A may be called tangential stress.
Q#26
A raindrop falls near the surface of the earth with almost uniform velocity because
(a) its weight is negligible
(b) the force of surface tension balances its weight
(c) the force of viscosity of air balances its weight
(d) the drops are charged and atmospheric electric field balances its weight.
Answer: (c)
When the raindrop starts falling the force of viscosity of air comes into action. This force is proportional to the velocity. Initially, this force is less than its weight. So there is a net downward force. Thus it accelerates. But a stage comes when due to increased velocity the force of viscosity is equal to its weight. So net downward force now becomes zero. Thus the raindrop keeps falling with a uniform velocity which is called the terminal velocity.
A piece of wood is taken deep inside a long column of water and released. It will move up
(a) with a constant upward acceleration
(b) with a decreasing upward acceleration
(c) with a deceleration
(d) with a uniform velocity.
Answer: (b)
Just when the wood is released, the net force on it is B-W, {Buoyancy minus weight}upward. If the mass of the wood be m, then it has an initial acceleration a =(B-W)/m. But as the velocity increases the viscous force V acts downward. So the net force becomes B-W-V. Though B and W are constant, V increases with the velocity. Thus as the wood moves up, the net force and hence the acceleration decreases.
Q#28
A solid sphere falls with a terminal velocity of 20 m/s in air. If it is allowed to fall in vacuum,
(a) terminal velocity will be 20 m/s
(b) terminal velocity will be less than 20 m/s
(c) terminal velocity will be more than 20 m/s
(d) there will be no terminal velocity.
Answer: (d)
The term, terminal velocity is associated with a falling object in a fluid where the force of viscosity balances the weight and buoyancy force. Since there is no medium in the vacuum, there is no viscosity to oppose the motion. So the solid sphere will keep accelerating and there will be no terminal velocity.
Q#29
A spherical ball is dropped in a long column of viscous liquid. the speed of the ball as a function of time may be best represented by the graph
(a) A
(b) B
(c) C
(d) D
Answer: (b)
When the ball falls in the long column of viscous liquid, it starts with zero speed and with a certain acceleration. As time passes its acceleration decreases with time.
In the speed time graph, the speed is zero at t = 0 only in graph A and B. The slope of the speed-time graph gives the acceleration. The slope of A is constant, that means the acceleration is constant which is not the case here.
The slope of the graph B decreases with time i.e. the acceleration decreases with time. Thus the motion of the ball is best represented by graph B.
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