Question:
A Physics teacher explains the concept of relative velocity to her students in class. She emphasises that when two bodies are moving in opposite directions, their relative velocity is sum of the velocities of the two. And when two bodies are moving in the same direction, their relative velocity is difference of the velocities of the two. Students are confused. The teacher then takes two balls one red and the other green. She says suppose red ball moves with a velocity of 5 m/s and green ball moves with a velocity of 4 m/s from a common point, and along the same straight line. If red ball is moving to the right and green ball is moving to the left, then after 1 sec, red ball is at R', where RR' = 5 m and green ball is at G' where GG' = 4 m, In Fig.(a).The distance between the two balls after 1 sec = G' R' = GG' + RR' = (4 + 5) = 9 m.
This is the magnitude of their relative velocity. If both the balls are moving to the right, as shown in Fig. (b), the distance between the two balls after 1 sec. = G' R' = RR' - GG' = 5 - 4 = 1 m.Read the above passage and answer the following questions :
(i) What value has the Physics teacher displayed ?
(ii) What have the students picked up?
(iii) Give at least one practical example of the concept.
Answer:
(i) The Physics teacher has displayed that giving practical illustration is a better way of driving home a difficult concept.
(ii) The students have picked up that learning,is faster and mote lasting with practical demonstration.And they should themselves follow this technique in their day to day life.
(iii) In practice,we find that head on collisions are far more disastrous than the collisions when two vehicles are moving in the same direction.This is because in the former case,relative velocity of vehicles is much larger than their relative velocity in the latter case.
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.
A particle moves over three quarters of a circle of radius r.What is the magnitude of its displacement ?
Q 4.
Write the three equations of uniformly accelerated motion. Give the meaning of each symbol in them.
Q 5.
What is represented by the graphs in Fig.?
.
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.
Why is a slight blow on a cork of bottle fully filled with a liquid sufficient to break the bottle ?
Q 8.
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 9.
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 10.
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 11.
Name the quantity that represents rate of change of velocity ?
Q 12.
A body starts from rest.What is zero ?
Q 13.
When will you say a body is in (i) uniform acceleration? (ii) nonuniform acceleration?
Q 14.
What will be the initial velocity of an object under free fall?
Q 15.
Under what conditions(s) is the magnitude of average
Q 16.
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 17.
What conclusion do you draw when displacement-time graph of a body is as shown in Fig.?
Q 18.
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 19.
What is pressure in case of fluids ? What is Pascal’s law ?
Q 20.
Why does a person feel pain when he stands on a pile of gravel than when he stands on a bed of sand ?
Q 21.
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 22.
What can you say about the motion of an object whose distance-time graph is a straight line parallel to the time axis ?
Q 23.
Draw speed-time graph for a body (i) at rest (ii) in uniform motion (iii) in uniformly accelerated motion.Discuss the results briefly.
Q 24.
A body thrown vertically upwards reaches a maximum height h.It then returns to ground.Calculate the distance travelled and the displacement.
Q 25.
A body is moving uniformly with a velocity of 5 m/s. Find graphically the distance travelled by it in 5 s.
Q 26.
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 27.
A trolley, while going down an inclined plane, has an acceleration of
starting from rest.What will be its velocity 3 s after the start ?
Q 28.
What is the relationship between the buoyant force on an object and the liquid displaced by it ?
Q 29.
An artificial satellite is moving in a circular orbit of radius 42250 km. Calculate its speed if it takes 24 hours to revolve around the Earth.
Q 30.
State velocity-time relation in uniformly accelerated motion. Use graphical method to obtain this relation.
Q 31.
A force of 16 N is distributed uniformly on one surface of a cube of edge 8 cm.Find the pressure on this surface.
Q 32.
Define buoyant force.What is its unit ?
Q 33.
Why is it easier to swim in sea water than in river water ?
Q 34.
When a plastic block is released under water,it never stays under water but instead comes to the surface of water.Explain why ?
Q 35.
Under what condition(s) is the magnitude of average velocity of an object equal to its average speed?
Q 36.
The following is the distancc-time table of a moving car.
(a) Use a graph paper to plot the distance travelled by the car versus the time.
(b) When was the car travelling at the greatest speed ?
(c) What is the average speed of the car ?
(d) What is the speed between 11.25 am and 11-40 am ?
(e) During a part of the journey, the car was forced to slow down to 12 km/h.At what distance did this
| Time | Distance |
|---|
10.05 am
10.25 am
10.40 am
10.50 am
11.00 am
11.10 am
11.25 am
11.40 am | 0 km
5 km
12km
22 km
26 km
28 km
38 km
42 km |
Q 37.
What is the acceleration of a body moving with uniform velocity ?
Q 38.
Explain the terms : uniform motion and non-uniform motion with examples.
Q 39.
Using velocity time graph,establish the relation s = ut +
,where the symbols have their usual meanings.
Q 40.
A cube of edge length 10 cm is placed inside a liquid.The pressure at the centre of the face is 15 Pa.Find the force exerted by the liquid on this face.
Q 41.
A car weighs 1200 kg.This weight is evenly distributed on 4 wheels.If the pressure in each tyre is
.what is the area of each tyre in contact.
Q 42.
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 43.
A weather forecasting plastic balloon of volume
contains hydrogen of density
.The mass of the empty balloon is 7.15 kg.Calcuiate (a) the mass or 'hydrogen in the balloon (b) Tne mass of balloon filled with hydrogen.
Q 44.
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 45.
A bottle can hold 100 g of water at 4°C.What mass of sea water (density =
) can it hold ?
Q 46.
Relative density of silver is 10.8.The density of water is
.What is the density of silver in SI units ?
Q 47.
A body of 2.0 kg floats in a liquid.What is the buoyant force on the body ?
Q 48.
The mass of a block made of certain material is 13 5 kg and its volume is
float or sink in water ? Give a reason for your answer.
Q 49.
Define thrust What is its unit ?
Q 50.
Define pressure.What is its unit ?
