Long Answer type questions
Question 1.
(a) Define momentum. Write its SI unit.
(b) A bullet of mass 0.02 kg is fired from a gun weighing 7.5 kg if the initial velocity of bullet is 200 m/s. Calculate the speed with which the gun recoils.
Answer
a. Momentum is defined as the product of mass and velocity and it is a vector quantity. SI unit of momentun is kg m/s
b. Applying law of conservation of momentum
$0=7.5v + .02 \times 200$
v=-.53 m/s
Question 2.
Why is it advised to tie the luggage with a rope on the roof buses?
Answer
Reason is given as
When a moving bus suddenly stops, the luggage on its roof still tends to continue in the state of motion due to inertia of motion. Thus, to avoid the falling of the luggage, it is tied with a rope on the roof of a bus.
Question 3.
State any three changes that a force brings about on a body. Give one example of each.
Answer
a. It can change the speed of the object. A ball slows down on the surface due to friction
b. it can change the direction of the object. In cricket,batsman hit the ball to change the direction of ball
c. It can change the shape of the object. Example stretched spring
Question 4.Tabulate two differences between balanced and unbalanced forces. Write one example of each.
Question 5.A book slides down a table top and comes to rest position after a certain distance. Name the force acting on the book. What types of forces are acting on the book? (Balanced/ unbalanced). Which force brought the book to rest?
Answer
When the book slides down the table top, two forces are acting
a. Friction force in upward direction
b. Gravitational force in downward direction.
The two forces are not equal and thus unbalanced force is there which moves the book downward.
Frictional force is responsible for bringing the book to rest position after certain distance after sliding
Question 6..
The mud particles sticking on the rim of a bicycle wheel leave the rim of the wheel tangentially when it starts moving. Explain.
Answer
This happens because of inertia of direction. When the bicycle wheel rotates, centripetal force is not exerted on the mud particles, so mud particles because of inertai of direction continue to move in straight line tangential to the wheel
Question 7.When a motor car makes a sharp turn at a high speed, we tend to get thrown to one side. Why?
Answer
This can again be explained on the basis of the law of inertia. We tend to continue in our straight-line motion. When an unbalanced force is applied by the engine to
change the direction of motion of the motorcar, we slip to one side of the seat due to the inertia of our body
Question 8..
What do you understand by inertia? Do all bodies have the same inertia? Illustrate giving an example.
Question 9..
State reason for the following:
a.A person is hit harder, when the person falls on a hard floor than when he falls on sand or cotton.
b.A gunman gets jerk in backward direction while firing a gun.
c.A bullet fired on a glass window makes a fine hole while a stone smashes when hits it.
Answer
a. In hard surface, the body comes to rest in shorter time the fall on cotton or sand, so force is more
b. The gun exerts force on the bullet.Now by Newton third law, an equal and opposite force acts on the gun and which is turn is exerted on the gunman
c. When the bullet strikes the glass window, the part of the glass window which comes in contact with the bullet immediately shares the large velocity of bullet and makes a hole, while the remaining part of the glass remains at rest and is therefore not smashed due to inertia of rest.
But when a slow moving stone strikes the same glass window, the various parts of the glass window gets enough time to share the velocity of the stone, and the glass is smashed.
Question 10.A passenger in a moving train tosses a coin which falls behind him. It means that motion of the train is
(a) accelerated
(b) uniform
(c) retarded
(d) along circular tracks
Answer
Answer is (a)
Question 11.
A stone of mass 1 kg is thrown with a velocity 20 m/s across the frozen surface of a lake and comes to rest after travelling a distance of 50 m. what is the force of friction between the stone and ice?
Answer
m=1 kg,u=20 m/s ,a=? , s=50 m ,v=0
$v^2 = u^2 + 2as$
a= -4 m/s^{2}
Force of friction = $1 \times 4 =4 N$
Question 12.
State Newton’s second law of motion and prove that Newton’s first law of motion is a special case of Newton’s second law of motion.
Question 13.
Answer the following:
(i) What is meant by momentum of a body? How can it be measured? Write its SI units.
(ii) Explain how does Newton’s first law give the qualitative definition of force?
Question 14.
Two objects A and B, having mass 100 kg and 75 kg, moving with velocity 40 km/hr and 6 km/hr respectively. Answer the following:
a.Which will have greater inertia?
b.Which will have greater momentum?
c.Which will stop first if equal negative acceleration is applied on both?
d.Which will travel greater distance?
e.Which will impart greater impulse if collides with a wall?
Answer
$M_a=100$ kg, $M_b=75$ kg , $v_a =40 km/hr$, $v_b=6 km/hr$
a. Now $M_a > M_b$, So Object A has more inertia
b. $p_a= M_a v_a= 4000 kg km/hr $, $p_b= M_b v_b= 450 kg km/hr $
Clearly $p_a > p_b$
c. Since velocity of object B is less then velocity of object A, Object B will stops first if equal negative acceleration is applied on both
d. Object A
e. Object A
Question 15.
(i) Define momentum. Write its SI unit.
ii) How much momentum will an object of mass 10 kg transfer to the floor if it falls from a height of 5 m? (g = 10 m/s
^{2})
(iii) Explain how a karate player can break a pile of tiles with a single blow of his hand.
Answer
ii. s= 5m , a= g=10 m/s^{2} ,u=0, v=?
$v^2= u^2+ 2as$
v= 10 m/s
Momentum of object when it touches the floor = $10 \times 10 = 100 kg m/s$
This same momentum will get tranferred to the floor
iii.karate player strikes the pile with his hand very fast. The large momentum of his hand is reduced to zero in a very short time. This exerts a large force on the pile of tiles which is sufficient to break them apart.
Question 16.A truck of mass M is moved under a force F. If the truck is then loaded with an object equal to the mass of the truck and the driving force is halved,then how does the acceleration change?.
Answer
Acceleration will be one -fourth
Question 17.
Do action and reaction act on the same body or on different bodies? Explain your answer with the help of example. How are they related in magnitude and direction? Write the total momentum of the gun and the bullet before firing.
Question 18.State reason for the following:
a.A runner presses the ground with his feet before he starts his run.
b.To take the boat away from the bank of a river, the boat man pushes the bank with an oar.
Answer
a. The runner pushes the ground with his feet and in turns , the ground applies the force on the runner to starts his run
b. When the boat manexerts a force of action on the bank with his ore, the bank exerts an equal and opposite force of reaction on the boat. Hence, the boat moves away from the bank.
Question 19.
Give an example to show that friction is an important factor in satisfying Newton’s third law of motion.
Question 20.
(a) State the law of conservation of momentum.
(b) A boy of mass 60 kg running at 3 m/s jumps on to a trolley of mass 140 kg moving with a velocity of 1.5 m/s in the same direction.
Find their common velocity.
Answer
By using law of conservation of momentum
$m_1 u_1 + m_2 u_2 = (m_1 + m_2) v$
$60 \times 3 + 140 \times 1.5 = (60 + 140)v$
v=1.95 m/s
Question 22.
A bullet of mass 10 g moving with a velocity of 400 m/s gets embedded in a freely suspended wooden block of mass 900 g. what is the velocity acquired by the block?
Answer
By using law of conservation of momentum
$m_1u_1 = (m_1 + m_2)v$
$.01 \times 400 = .91 v$
v=4.39 m/s
Question 24.
A man weighing 60 kg runs along the rails with a velocity of 18 km/h and jumps into a car of mass 1 quintal (100 kg) standing on the rails. Calculate the velocity with which car will start travelling along the rails.
Answer
Here m= 60 kg ,u_{1}= 18 km/hr = 5 m/s , M=100 kg ,u_{2}=0
Let v be the velocity with car start travelling
Now
$mu_1 + Mu_2 = (M+m)v$
$ 60 \times 5 = 160 v$
v= 1.875 m/s
Question 25.
State the law of conservation of momentum.
Using this law explain why a gun recoils.
Question 26.
A stone released from the top of a tower of height 19.6 m, calculate its final velocity just before touching the ground. (Take g = 9.8 m/s
^{2})
Answer
s= 19.6 m , u=0, a= 9.8 m/s^{2} ,v=?
$v^2 = u^2 + 2as$
v= 19.6 m/s
Question 27.
A boy of mass 50 kg running 5 m/s jumps on to a 20 kg trolley travelling in the same direction at 1.5 m/s. find their common velocity.
Answer
Here m=50 kg ,$u_1 = 5m/s$ ,M= 20 kg ,$u_2=1.5 m/s$
Now
$mu_1 + M u_2 = (M+m)v$
$ 50 \times 5 + 20 \times 1.5 = 70 v$ v
or v= 4 m/s
Question 28.
Car A of mass 1500 kg travelling at 25 m/s collides with another car B of mass 1000 kg travelling at 15 m/s in the same direction. After collision, the velocity of car A becomes 20 m/s. Calculate the velocity of car B after collision.
Answer
Here $m_1=1500kg$,$u_1=25 m/s$,$m_2=1000kg$, $u_2=15m/s$ ,$v_1=20 m/s$ ,$v_2=?$
Now
$m_1u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$
$1500 \times 25 + 1000 \times 15 = 1500 \times 20 + 1000v$
v=22.5 m/s
Law of Conservation of Momentum Long answer type questions
Question 1.
(a) State law of conservation of momentum. Write SI unit of momentum.
(b) Two cars each of mass 1000 kg are moving in a straight line but in opposite directions. The velocity of each car is 5 m/s before the collision during which they stick together. What will be the velocity of the combined cars after collision?
Answer
b. As per law of conservation of momentum
$1000 \times 5 - 1000 \times 5 = 2000v$
or v=0
Question 2.
(a) Define momentum. Write its SI unit.
(b) A car and a truck have same momentum. Whose velocity is more and why?
(c) A bullet of mass 20 g moving with a speed of 500 m/s strikes a wooden block of mass 1 kg and gets embedded in it. Find the speed with which block moves along with the bullet.
Answer
a. $p=mv$ and SI unit is kg m/s
b. Since car is having less mass then truck ,velocity of car will be more
c. m= 20 g= .002 kg ,u=500 m/s , M= 1kg
Now
$mu = (M+m) v$
$ .02 \times 500 = (1.02) v$
or v= 9.8 m/s
Question 3.
Prove the law of conservation of momentum with clear explanation, diagram and equation.
Question 4.
(a) State law of conservation of momentum. Express it mathematically, when two bodies of masses $m_1$ and $m_2$ moving in same direction along same straight line with velocities $u_1$ and $u_2$ respectively, collide and their respective velocities after collision become $v_1$ and $v_2$.
(b) A hammer of mass 500 g moving with 50 m/s strikes a nail. The nail stops the hammer in a small time interval of 0.01/s. what is the change in momentum suffered by the hammer? Also calculate the force of the hammer on the nail. What will be the force of the nail on the hammer? Give reason for your answer.
Answer
a. As per law of conservation of momentum, When two or more bodies acts upon each other their total momentum remains constant provided no external forces are acting
Initial Momentum
$p_1 = m_1 u_1 + m_2 u_2$
Final Momentum
$p_2 = m_1 v_1 + m_2 v_2$
Now
$p_1 =p_2$
$m_1 u_1 + m_2 u_2= m_1 v_1 + m_2 v_2$
b. m= 500g = .5 kg , u=50 m/s ,t=.01 s, v=0 ,a=?
$\Delta p = p_2 - p_1 = mv - mu= -25 kg m/s
$v=u+at$
a=-5000 m/s^{2}
Force of Hammer=$ ma= .5 \times 5000= 2500 N$
Force of Nail= Force on Hammer= 2500N
Question 5.Name and define the various types of inertia. Illustrate each of them with suitable example.
Answer
We have basically three types of Inertia-:
(a) Inertia of Rest: This is the resistance offered by body to change its state of rest
Examples:
(i) Person sitting in a car falls backwards, when the car suddenly starts. It is because the lower portion in contact with the car comes in motion where as the upper part tries to remain at rest due to inertia of rest.
(ii)When a carpet is beaten with a stick then the dust particles due to inertia of rest tends to remain in rest while the fibers of carpet becomes in motion.
(b) Inertia of Motion:This is the resistance offered by body to change of uniform motion is known as Inertia of motion.
Examples:
(i) When a moving car suddenly stops the person sitting in the car falls forward because the lower portion of the body in contact with the car comes to rest whereas the upper part tends to remain in motion due to inertia of motion.
(ii) An athlete runs a certain distance before taking a long jump because the velocity acquired by running is added to the time of jump, so that it can cover a long distance.
(c) Inertia of Direction: This is the resistance offered by body to change its direction of motion.
Examples:
(i) When a car moves round a curve the person sitting inside is thrown outwards in order to maintain his direction of motion due to inertia of motion
Question 6.(i) Define momentum. State its SI unit.
(ii) An object of mass 50 kg is accelerated uniformly from a velocity of 4 m/s to 8 m/s in 8 s. calculate the initial and final momentum of the object. Also find the magnitude of the force exerted on the object.
Answer
i. Momentum is defined as the product of mass and velocity and it is a vector quantity. SI unit of momentun is kgm/s
ii. u= 4 m/s ,v=8 m/s ,t=8 sec, a=?
$v=u+at$
a= .5 m/s^{2}
Initial Momentum = $50 \times 4 = 200 kgm/s$
Final Momentum = $50 \times 8 = 400 kgm/s$
Force exerted = $ma = 50 \times .5 = 25 N$
INTERESTING NUMERICALS
Question 1.
A bullet of 10 g strikes a sand bag at a speed of 10
^{3} m/s and gets embedded after travelling 5 cm. Calculate
(i) the resistive force exerted by the sand on the bullet.
(ii) the time taken by the bullet to come to rest.
Answer
i. u=10^{3} m/s ,v=0 ,s=5 cm= .05 m ,a=?
$v^2=u^2 + 2as$
a=- 10^{7} m/s
Resistive force on bullet = $.001 \times 10^7= 10^5 N$
ii. $v=u+at$
t=10^{4}s
Question 2.
A force of 5 N produces an acceleration of 8 m/s
^{2} on a mass $m_1$ and an acceleration of 24 m/s
^{2} on a mass $m_2$. What acceleration would the same force provide if both the masses are tied together?
Answer
From Force formula
$F=ma$
$5=8m_1$ or $m_1= \frac {5}{8}$
and $5= 24m_2$ or $m_2 = \frac {5}{24}$
Now when the two masses are tied and same force is applied, acceleration will be
$a = \frac {F}{m_1+ m_2} = \frac {5}{\frac {5}{8} + \frac {5}{24}} = 6 m/s^2$
Question 3.
A hammer of mass 500 g, moving at 50 m/s, strikes a nail. The nail stops the hammer in a very short time of 0.01 s. what is the force of the nail on the hammer?
Answer
Acceleration of the Hammer is given by
$a = \frac {v-u}{t} = \frac {0- 50}{.01}= -5000 m/s^2$
Force is given by
$F=ma = .5 \times 5000 = 2500N$
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