Forces and Laws of Motion
Momentum
Numertical Problems Based on Momentum
Type – I – (Calculation of Momentum)
Question:-
1 - What will be the momentum of a stone having mass of 10 kg when it is thrown
with a velocity of 2m/s?
Solution:-
Given,
Mass (m)
= 10kg
Velocity
(v) = 2m/s
Momentum
(p) =?
We know
that, Momentum (p) = Mass (m) x Velocity (v)
Therefore,
p = 10kg x 2 m/s = 20 kg m/s
Thus the
momentum of the stone = 20 kg m/s.
Question:
2 - Calculate the momentum of a bullet of 25 g when it is fired from a gum with
a velocity of 100m/s.
Solution:
Given,
Velocity
of the bullet (v) = 100m/s
Mass of
the bullet (m) = 25 g = 25/1000 kg = 0.025kg
Momentum
(p) =?
Or, p =
2.5 kg m/s
Thus the
momentum of the bullet = 2.5 kg m/s
Question:
3 - Calculate the momentum of a bullet having mass of 25 g is thrown using hand
with a velocity of 0.1 m/s.
Solution:
Given,
Velocity
of the bullet (v) = 0.1m/s
Mass of
the bullet (m) = 25 g = 25/1000 kg = 0.025kg
Momentum
(p) =?
We know
that, Momentum (p) = Mass (m) x Velocity (v)
Therefore,
p = 0.025 kg x 0.1 m/s
Or, p =
0.0025 kg m/s
Thus the
momentum of the bullet = 0.0025 kg m/s
Question:
4 - The mass of a goods lorry is 4000 kg and the mass of goods loaded on it is
20000 kg. If the lorry is moving with a velocity of 2m/s what will be its
momentum?
Solution:
Given,
Velocity
(v) = 2m/s
Mass of
lorry = 4000 kg, Mass of goods on the lorry = 20000 kg
Therefore,
total mass (m) of the lorry = 4000 kg + 20000 kg = 24000 kg
Momentum
(p) =?
We know
that, Momentum (p) = Mass (m) x Velocity (v)
Therefore,
p =
24000 kg x 2 m/s = 48000 kg m/s
Thus,
momentum of the lorry = 48000 kg m/s
Question:
5 - A car having mass of 1000 kg is moving with a velocity of 0.5m/s. What will
be its momentum?
Solution:
Given,
Velocity
of the bullet (v) = 0.5m/s
Mass of
the bullet (m) = 1000 kg
Momentum
(p) =?
We know
that, Momentum (p) = Mass (m) x Velocity (v)
Therefore,
p = 1000 kg x 0.5 m/s
Or, p =
500 kg m/s
Thus the
momentum of the bullet = 500 kg m/s
Type – II (Calculation of Mass)
Question:
1 – A vehicle is running with a velocity of 5m/s. If the momentum of the
vehicle is 5000 kg m/s, what is its mass?
Solution:
Given,
Momentum
(p) = 5000 kg m/s
Velocity
(v) = 5m/s
Mass (m)
=?
We know
that, Momentum (p) = Mass (m) x Velocity (v)
Therefore,
5000 kg m/s = m × 5m/s
m = 5000 kg m/s = 1000 kg
5 m/s
Thus,
mass of the vehicle = 1000 kg
Question:
2 – A stone attains a momentum of 1 kg m/s when it flies with a velocity of
2m/s, then what will be mass of the stone?
Solution:
Given,
Momentum
(p) = 1 kg m/s
Velocity
(v) = 2m/s
Mass (m)
=?
We know that,
Momentum (p) = Mass (m) x Velocity (v)
Therefore,
1 kg m/s = m × 2m/s
m = 1kg m/s = 0.5 kg = 500 gm
2 m/s
Thus,
mass of the stone = 0.5 kg or 500 g
Question:
3 – When a bullet is fired from a rifle its momentum become 20 kg m/s. If the
velocity of the bullet is 1000m/s what will be its mass?
Solution:
Given,
Momentum
(p) = 20 kg m/s
Velocity
(v) = 1000m/s
Mass (m)
=?
We know
that, Momentum (p) = Mass (m) x Velocity (v)
Therefore,
20 kg m/s = m × 1000m/s
m = 20 kg m/s = 1 kg = 0.02 Kg = 20 gm
1000 m/s 50
Thus,
mass of the bullet = 20 g
Question:
4 – When a missile is fired from a tank it gets a momentum of 2000 kg m/s. If
the velocity of the missile is 50m/s what will be its mass?
Solution:
Given,
Momentum
(p) = 2000 kg m/s
Velocity
(v) = 50m/s
Mass (m)
=?
We know
that, Momentum (p) = Mass (m) x Velocity (v)
Therefore,
2000 kg m/s = m × 50 m/s
m = 2000 kg m/s = 40 kg
50 m/s
Thus,
mass of the missile = 40 g
Question:
5 – A bird is flying with a velocity of 3 m/s. If the momentum of the bird is
3.60 kg m/s what is its mass?
Solution:
Given,
Momentum
(p) = 3.60 kg m/s
Velocity
(v) = 3 m/s
Mass (m)
=?
We know
that, Momentum (p) = Mass (m) x Velocity (v)
Therefore,
3.60 kg m/s = m × 3 m/s
m = 3.60 kg m/s = 1.20 kg = 1 kg 200gm
3 m/s
Thus,
mass of the bird = 1 kg 200 g
Type – III (Calculation of velocity)
Question:
1 – If the momentum of a flying brick is 50 kg m/s and its mass is 10 kg.
Calculate its velocity?
Solution:
Given,
Momentum
(m) = 50kg m/s
Mass (m)
= 10kg
Velocity
(v) =?
We know
that,
Momentum
(p) = Mass (m) x Velocity (v)
⇒ 50 kg m/s = 10kg × v
v = 50 kg m/s = 5 m/s
10 kg
Thus,
velocity of the brick = 5m/s
Question:
2 – A bullet of 25 g is when fired from a piston gets a momentum of 50 kg m/s.
Calculate the velocity of bullet.
Solution:
Given,
Momentum
(m) = 50kg m/s
Mass (m)
= 25 g = 25/1000 kg = 0.025 kg
Velocity
(v) =?
We know
that,
Momentum
(p) = Mass (m) x Velocity (v)
⇒ 50 kg m/s = 0.025 kg × v
v = 50 kg m/s = 2000 m/s
0.025 kg
Thus,
velocity of the bullet = 2000 m/s
Question:
3 – A vulture when flying with a velocity ‘v’ attains a momentum of 20 kg m/s.
If the mass of the vulture is 25 kg what is the value of ‘v’?
Solution:
Given,
Momentum
(m) = 20 kg m/s
Mass (m)
= 25 kg
Velocity
(v) =?
We know
that, Momentum (p) = Mass (m) x Velocity (v)
⇒ 20 kg m/s = 25 kg × v
v = 20 kg m/s =0.8 m/s
25 kg
Thus,
velocity of the vulture = 8 m/s
Question:
4 – A brick after falling from a hill collide with ground with a momentum of
100 kg m/s. If the mass of the brick is 5 kg what was its velocity while
colliding with the ground?
Solution:
Given,
Momentum
(m) = 100kg m/s
Mass (m)
= 5kg
Velocity
(v) =?
We know
that,
Momentum
(p) = Mass (m) x Velocity (v)
⇒ 100 kg m/s = 5kg × v
v = 100 kg m/s = 20 m/s
5 kg
Thus,
velocity of the brick = 20 m/s
Question:
5 – Calculate the velocity of a missile having mass of 100 kg, if it attains a
momentum of 5000 kg m/s when fired from a rocket gun?
Solution:
Given,
Momentum
(m) = 5000kg m/s
Mass (m)
= 100kg
Velocity
(v) =?
We know
that, Momentum (p) = Mass (m) x Velocity (v)
⇒ 5000 kg m/s = 100kg × v
v = 5000 kg m/s = 50 m/s
100 kg
Thus,
velocity of the missile = 50 m/s
NCERT In Text Solution
Question:-
1 - Which of the following has more inertia:
(a) a
rubber ball and a stone of the same size?
(b) a
bicycle and a train?
(c) a
five rupees coin and a one-rupee coin?
Answer:-
(a) A
stone.
(b) A
train
(c) A
five rupees coin.
Explanation
– Inertia is associated with mass. Objects having more mass have more inertia.
Question:-
2 - In the following example, try to identify the number of times the velocity
of the ball changes:
“A
football player kicks a football to another player of his team who kicks the
football towards the goal. The goalkeeper of the opposite team collects the
football and kicks it towards a player of his own team”. Also identify the
agent supplying the force in each case.
Answer:
The
velocity of football changes four times.
First,
when a football player kicks to another player, second when that player kicks
the football to the goalkeeper. Third when the goalkeeper stops the football.
Fourth when the goalkeeper kicks the football towards a player of his own team.
Agent
supplying the force –
First
case – First player
Second
case – Second player
Third
case – Goalkeeper
Fourth
case – Goalkeeper
Question:
3 - Explain why some of the leaves may get detached from a tree if we
vigorously shake its branch.
Answer:
The answer of this cause lies behind the Newton’s First Law of Motion.
Initially, leaves and tree both are in rest. But when the tree is shaken
vigorously, tree comes in motion while leaves have tendency to be in rest.
Thus, because of remaining in the position of rest some of the leaves may get
detached from a tree if we vigorously shake its branch.
Question:
4 - Why do you fall in the forward direction when a moving bus brakes to a stop
and fall backwards when it accelerates from rest?
Answer:
In a
moving bus, passengers are in motion along with bus. When brakes are applied to
stop a moving bus, bus comes in the position of rest. But because of tendency
to be in the motion a person falls in forward direction.
Similarly,
when a bus is accelerated from rest, the tendency to be in rest, a person in
the bus falls backwards.
Question:
5 - If action is always equal to the reaction, explain how a horse can pull a
cart.
Answer:
Horse pushes the ground in backward direction. In reaction to this, the horse
moves forward and cart moves along with horse in forward direction.
In this
case when horse tries to pull the cart in forward direction, cart pulls the
horse in backward direction, but because of the unbalanced force applied by the
horse, it pulls the cart in forward direction.
Question:
6 - Explain, why is it difficult for a fireman to hold a hose, which ejects
large amounts of water at a high velocity.
Answer:
When large amount of water is ejected from a hose at a high velocity, according
to Newton’s Third Law of Motion, water pushes the hose in backward direction
with the same force. Therefore, it is difficult for a fireman to hold a hose in
which ejects large amount of water at a high velocity.
