Question:
(a)Which human virtue was at stake when Archimedes came out with his principle while bathing in a tub ?
(b) Briefly discuss three cases where Archimedes Principle is at work.
Answer:
(a) Honesty because Archimedes was to test the purity of gold in a crown without disfiguring it.
(b)(i) A subsmarine has a large ballast tank,which is used to control its position and depth from the surface of the sea.It submerges by letting water into the ballast tank so that its weight becomes greater than the buoyant force (and vice versa).It floats by reducing water in the ballast tank so that its weight becomes less than the buoyant force.
(ii) A certain group of fish uses Archimedes Principle to go up and down the water.To go up to the surface, the fish fills up its swim bladder (air sacs) with gases.The gases diffuse from its own body to the bladder, thus making its body lighter. This enables the fish to go up.To go down,the fish empties its bladder,thereby increasing its density.
(iii) A ship floats on the surface of the sea because the volume of water displaced by the ship is enough to have a weight equal to the weight of the ship.(A ship floats higher in cold water than in warm water as cold water has a relatively higher density).
Motion
Q 1.
Derive graphically the equation of motion for position-velocity relation of a body moving with uniform acceleration.
Q 2.
A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds?
Q 3.
When will you say a body is in (i) uniform acceleration? (ii) nonuniform acceleration?
Q 4.
A cyclist cycles for t second at a speed of 3 m/s and then for the same time at a speed of 5 m/s along a straight road due north. What is the average speed of the cyclist?
Q 5.
A particle moves over three quarters of a circle of radius r.What is the magnitude of its displacement ?
Q 6.
The mass of an empty 40 litre petrol tank of a vehicle is 8.0 kg.What will be its mass when filled completely with a fuel of density 700
Q 7.
What is represented by the graphs in Fig.?
.
Q 8.
Write the three equations of uniformly accelerated motion. Give the meaning of each symbol in them.
Q 9.
Calculate the greatest and the least pressure exerted by a metal block of size 20 cm x 8 cm x 5 cm and having a mass of 5 kg.
Q 10.
Why is a slight blow on a cork of bottle fully filled with a liquid sufficient to break the bottle ?
Q 11.
A ship is moving at a speed of 56 km/h.One second later,it is moving at 58 km/h.What is its acceleration ?
Q 12.
A body starts from rest.What is zero ?
Q 13.
What will be the initial velocity of an object under free fall?
Q 14.
Under what conditions(s) is the magnitude of average
Q 15.
What is pressure in case of fluids ? What is Pascal’s law ?
Q 16.
What conclusion do you draw when displacement-time graph of a body is as shown in Fig.?
Q 17.
Draw speed-time graph for a body (i) at rest (ii) in uniform motion (iii) in uniformly accelerated motion.Discuss the results briefly.
Q 18.
A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg.The area of the piston carrying the load is
.What maximum pressure would the smaller piston have to bear ?
Q 19.
Define buoyant force.What is its unit ?
Q 20.
What is the relationship between the buoyant force on an object and the liquid displaced by it ?
Q 21.
Air is a fluid and our bodies displace air.As a result of this,a buoyant force is acting on each one of us.
(a)What is the approximate density of your body ?
(b) What is your approximate volume ?
(c) Estimate the magnitude of the buoyant force on you due to the air displaced.Consider your mass to be 75 kg.
(d)Does it mean that your weight is more than the scale reading ?
(Given density of air,pa =
)
Q 22.
Name the quantity that represents rate of change of velocity ?
Q 23.
If velocity-time graph of a body is as shown in Fig.,what is the nature of motion ?
Q 24.
Why does a person feel pain when he stands on a pile of gravel than when he stands on a bed of sand ?
Q 25.
When a plastic block is released under water,it never stays under water but instead comes to the surface of water.Explain why ?
Q 26.
What can you say about the motion of an object whose distance-time graph is a straight line parallel to the time axis ?
Q 27.
State velocity-time relation in uniformly accelerated motion. Use graphical method to obtain this relation.
Q 28.
A bottle can hold 100 g of water at 4°C.What mass of sea water (density =
) can it hold ?
Q 29.
What force acting on an area of
will produce a pressure of 500 Pa ?
Q 30.
The density of turpentine oil is
.What will be its relative density ?
Q 31.
Why is it easier to swim in sea water than in river water ?
Q 32.
A car travels along a straight line for first half time with speed 40 km/h and the second half time with speed 60 km/h. Find the average speed of the car.
Q 33.
A train starting from rest moves with a uniform acceleration of 0.2
for 5 minutes.Calcualte the speed acquired and the distance travelled in this time.
Q 34.
A farmer moves along the boundary of a square field of side 10 m in 40 s.What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds ?
Q 35.
A stone is thrown in a vertically upward direction with a velocity of 5 m/s. If the acceleration of the stone during its motion is
in the downward direction,what will be the height attained by the stone and how much time will it take to reach there ?
Q 36.
The speed-time graph for a car is shown is Fig.
(a) Find how far does the car travel in the first 4 seconds.Shade the area on the graph that represents the distance travelled by the car during this period.
(b) Which part of the graph represents uniform motion of the car ?
.
Q 37.
Use graphical method to derive the relation
-
= 2 as,where the symbols have their usual meanings.
Q 38.
Calculate the mass of air enclosed in a room of length,breadth and height equal to 5 m, 3 m and 4 m respectively.Density of air =
.
Q 39.
The mass of a density bottle is 25 g when empty, 50 g when filled completely with water and 365 g when filled completely with mercury. Find the density of mercury.
Q 40.
Calculate the pressure when a force of 200 N acts on an
Q 41.
What is Archimedes’ Principle ? How can it be experimentally verified ?
Q 42.
What is meant by scalars and vectors?
Q 43.
A particle moves along the x axis from A to B. Which Of the following values of the initial and final coordinates, which results in a negative displacement?
(a) A = 4m, B = 6m
(b) A = −4m, B = −2m
(c) A = −4m, B = −8m
(d) A = −4m, B = 2m
Q 44.
A bus starting from rest moves with a uniform acceleration of 0.1 ms–2 for 2 minutes.
Find (a) the speed acquired, (b) the distance travelled.
Q 45.
The equation S = ut + ½at2 gives information as
(a) velocity is a function of time.
(b) velocity is a function of position.
(c) Position is a function of time.
(d) Position is function of velocity and time.
Q 46.
Mathematically prove that the distance (S) travelled by an object is the average mean of initial velocity(u) and final velocity(v) having constant acceleration(a) in the direction of motion in a straight line.
Q 47.
A body thrown vertically upwards reaches a maximum height h.It then returns to ground.Calculate the distance travelled and the displacement.
Q 48.
A body travels a distance of 15 m from A to B and then moves a distance of 20 m at right angles to AB.Calculate the total distance travelled and the displacement.
Q 49.
A train travels some distance with a speed of 30 km/h and returns with a speed of 45 km/h.Calculate the average speed of the train.
Q 50.
A car accelerates uniformly from 18 km/h to 36 km/h in 5 second. Calculate (i) the acceleration and (ii)the distance covered by the car in that time.
