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Wednesday, September 15, 2010
Wednesday, September 8, 2010
Numericals assignment- class IX
Q What is the momentum of a man of mass 75kg when he walks with a uniform velocity of 2m/s?
Q What is change in momentum of a car weighing 1500 kg when its speed increases from 36km/h to 72km/h uniformly?
Q A man throws a ball weighing 500g vertically upwards witha speed of 10m/s.
1) what will be its initial momentum?
2) What would be its momentum at the highest point of his flight?
Q A truck starts from rest and rools down a hill with constant acceleration. It travels a distance of 400m in 20s. Find the force acting on it if its mass is 7 metric tonnes. ( 1 metric ton= 1000kg)
Q A car of mass 2400kg moving with a velocity of 20m/s is stopped in 10s on applying brakes. Calculate the retardation and the retarding force.
Q For how long should a force of 100N act on a body of 20kg so that it acquires a velocity of 100m/s?
Q A body of mass 2kg is at rest. What should be the magnitude of force which will make the body move with a speed of 30m/s at the end of 1s?
Q An unloaded truck weighing 2000kg has a maximum acceleration of 0.5 m/s*s. What is the maximum acceleration when it is carrying a load of 2000kg?
Q The car A of mass 1500kg, travelling at 25m/scollides with another car B of mass 1000kg travelling at 15m/s in the same direction. After collision the velocity of car A becomes 20m/s. Calculate the velocity of car B after collision.
Q A bullet of mass 10g moving with a velocity of 400m/s gets embedded in a freely suspended wooden block of mass 900g. What is the velocity acquired by the block?
Q A 10g bullet travelling at 200m/s strikes and remains embedded in a 2kg target which is originally at rest but free to move. At what speed does the target move off?
Q A gun of mass 3kg fires a bullet of mass 30g. The bullet takes 0.003s to move through the barrel of the gun and acquires a velocity of 100m/s. calculate:
a) the velocity with which the gun recoils.
b) the force exerted on gunman due to recoil of the gun.
Q A ball X of mass 1kg trvelling at 2m/s has a head on collision with an identical ballY at rest. X stops and Y moves off. Calculate the velocity of Y after the collision.
Q A boy of mass 50kg running at 5m/s jumps onto a 20kg trolley travelling in the same directionat 1.5m/s. What is their common velocity?
Q A girl of mass 50kg jumps out of a rowing boat of mass 300kg on to the bank, with ahorizontal velocity of 3m/s. With what velocity does the boat begin to move backwards?
Q The velocity of a body of mass 10kg increases from 4m/s to 8m/s when a force acts on it for 2s.
a) What is the momentum before the force acts?
b) What is the momentum after the force acts?
c) What is the gain in momentum per second?
d) What is the value of the force?
Q Calculate the value of acceleration due to gravity on the surface of the moon?
Q The earth's gravitational force causes an acceleration of 5m/s*s in a 1kg mass somewhere in space. How much will the acceleration of a 3kg mass be at the same place?
Q To estimate the height of a bridge over a river, a stone is dropped freely in river from bridge. The stone takes 2s to touch the water surface. Calculate the height of bridge from the water level.
Q A cricket ball is dropped from a height of 20m
a) Calculate the speed of the ball when it hits the ground.
b) Calculate the time it takes to fall through this height.
Q A body has a weight of 10kg on the surface of the earth. What will be its weight when taken to the centre of the earth?
Q A stone resting on the ground has a gravitational force of 20N acting on it. What is the weight of the stone
Q What is change in momentum of a car weighing 1500 kg when its speed increases from 36km/h to 72km/h uniformly?
Q A man throws a ball weighing 500g vertically upwards witha speed of 10m/s.
1) what will be its initial momentum?
2) What would be its momentum at the highest point of his flight?
Q A truck starts from rest and rools down a hill with constant acceleration. It travels a distance of 400m in 20s. Find the force acting on it if its mass is 7 metric tonnes. ( 1 metric ton= 1000kg)
Q A car of mass 2400kg moving with a velocity of 20m/s is stopped in 10s on applying brakes. Calculate the retardation and the retarding force.
Q For how long should a force of 100N act on a body of 20kg so that it acquires a velocity of 100m/s?
Q A body of mass 2kg is at rest. What should be the magnitude of force which will make the body move with a speed of 30m/s at the end of 1s?
Q An unloaded truck weighing 2000kg has a maximum acceleration of 0.5 m/s*s. What is the maximum acceleration when it is carrying a load of 2000kg?
Q The car A of mass 1500kg, travelling at 25m/scollides with another car B of mass 1000kg travelling at 15m/s in the same direction. After collision the velocity of car A becomes 20m/s. Calculate the velocity of car B after collision.
Q A bullet of mass 10g moving with a velocity of 400m/s gets embedded in a freely suspended wooden block of mass 900g. What is the velocity acquired by the block?
Q A 10g bullet travelling at 200m/s strikes and remains embedded in a 2kg target which is originally at rest but free to move. At what speed does the target move off?
Q A gun of mass 3kg fires a bullet of mass 30g. The bullet takes 0.003s to move through the barrel of the gun and acquires a velocity of 100m/s. calculate:
a) the velocity with which the gun recoils.
b) the force exerted on gunman due to recoil of the gun.
Q A ball X of mass 1kg trvelling at 2m/s has a head on collision with an identical ballY at rest. X stops and Y moves off. Calculate the velocity of Y after the collision.
Q A boy of mass 50kg running at 5m/s jumps onto a 20kg trolley travelling in the same directionat 1.5m/s. What is their common velocity?
Q A girl of mass 50kg jumps out of a rowing boat of mass 300kg on to the bank, with ahorizontal velocity of 3m/s. With what velocity does the boat begin to move backwards?
Q The velocity of a body of mass 10kg increases from 4m/s to 8m/s when a force acts on it for 2s.
a) What is the momentum before the force acts?
b) What is the momentum after the force acts?
c) What is the gain in momentum per second?
d) What is the value of the force?
Q Calculate the value of acceleration due to gravity on the surface of the moon?
Q The earth's gravitational force causes an acceleration of 5m/s*s in a 1kg mass somewhere in space. How much will the acceleration of a 3kg mass be at the same place?
Q To estimate the height of a bridge over a river, a stone is dropped freely in river from bridge. The stone takes 2s to touch the water surface. Calculate the height of bridge from the water level.
Q A cricket ball is dropped from a height of 20m
a) Calculate the speed of the ball when it hits the ground.
b) Calculate the time it takes to fall through this height.
Q A body has a weight of 10kg on the surface of the earth. What will be its weight when taken to the centre of the earth?
Q A stone resting on the ground has a gravitational force of 20N acting on it. What is the weight of the stone
Gravitation- Class IX
Q According to Universal law of gravitation- every body on the earth attracts every other body with a gravitational force, why then this force does not cause any motion in the objects?
Ans Though the various objects on this earth constantly attract each other, they do not cause any motion because-
1) Each body experiences multiple forces from different directions and most of these forces get cancelled from each other.
2) The gravitational force of attraction between them is very small due to their comparatively small masses.
Ans Though the various objects on this earth constantly attract each other, they do not cause any motion because-
1) Each body experiences multiple forces from different directions and most of these forces get cancelled from each other.
2) The gravitational force of attraction between them is very small due to their comparatively small masses.
Gravitation and Newton's laws of motion
According to Third law of motion every action has equal and opposite reaction. This means that if earth attracts a body towards it witha force,F then the body also attracts earth with same force but in opposite direction i.e. -F. But we know that earth does not move towards the object because according to second law of motion, F=ma
a=F/m
As we see that acceleration is inversely proportional to m, therefore a negligible acceleration is produced in earth due to its high mass.
Acceleration due to gravity
If we drop a body of mass 'm' from a distance 'R' from centre of earth of mass 'M', then earth will exert a force of gravitation on the body,F
F=G M m/R*R - 1
According to second law of motion, F=ma -2
Equating 1 and 2
GMm/R*R = ma
a= GM/R*R
Since we know that in case of free fall, a= g (acceleration due to gravity),
g= GM/R*R
Putting values, we get g=9.8 m/s*s
Dependence of acceleration due to gravity
1) Since acceleration due to gravity is independent of mass of object i.e. 'm', therefore, both light and heavy objects are accelerated by same amount.
2) As 'g' depends on 'R', the value of 'g' varies at poles and equator. Since, 'R' is more at equator, 'g' is small at equator and 'R' is less at poles, therefore, 'g' is more at poles.
Weight on moon
Let We= weight on earth and Wm= weight on moon
Wm= GM*m/R*R where M is mass of moon, m is mass of object and R is radius of moon
Now, mass of earth is 100 times mass of moon and radius of earth is 4 times radius of moon
We= G 100M*m/4R*4R
We= 100GmM/16R*R
Wm/We= 16/100
or approximately, Wm/We=1/6
Therefore, weight of an object on moon is 1/6th of weight of that object on earth.
Difference between mass and weight
Mass
1) The mass of an object is the quantity of matter contained in it.
2) The S.I. unit of mass is kilogram (kg).
3) The mass of an object is constant.
4) The mass of an object can never be zero.
Mass
1) The mass of an object is the quantity of matter contained in it.
2) The S.I. unit of mass is kilogram (kg).
3) The mass of an object is constant.
4) The mass of an object can never be zero.
Weight
1) The weight of an object is the force with which it is attracted towards the centre of the earth.
2) The S.I. unit of weight is Newton (N).
3) The weight of an object is not constant. It changes with the change in acceleration due to gravity (g).
4) The weight of an object can be zero. e.g. in the interplanetary space, where g=0, the weight of an object becomes zero.
1) The weight of an object is the force with which it is attracted towards the centre of the earth.
2) The S.I. unit of weight is Newton (N).
3) The weight of an object is not constant. It changes with the change in acceleration due to gravity (g).
4) The weight of an object can be zero. e.g. in the interplanetary space, where g=0, the weight of an object becomes zero.
Equations of motions for freely falling bodies
1) v=u+gt
2) h=ut+ 1/2gt*t
3) v*v= u*u+ 2gh
IMPORTANT POINTS TO REMEMBER
1) The physical quantities having vertically upward motion are assigned +ve values whereas the physical quantities having downward motion are assigned -ve values.
2) The acceleration due to gravity of earth is always taken -ve.
3) When a body is dropped freely from a height, its initial velocity 'u' is zero.
4) When a body is thrown vertically upwards, its final velocity 'v' becomes zero.
5) The time taken by a body to rise to the highest point is equal to the time it takes to fall from the same height.
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