Forces and Laws of Motion Test

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Forces and Laws of Motion Test - 43

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Question 1
1 / -0

Consider the following statements:
(a) No net force acts on a rain drop falling vertically with a constant speed.
(b) If net force acting on the body is zero, momentum of the body remains constant.
(c) Particle of different masses falls with different acceleration on earth.
(d) It is easier to start motion in a heavier body than a lighter body.
Which of the above statements are correct?

A
(b) and (c)

B
(a) and (b)

C
(a), (b) and (d)

D
All of the above

Solution

Rain drop is falling vertically with constant velocity, then no net force is acting on the rain drop.
Net force equals to zero implies, rate of changes of momentum is zero which means momentum is not changing with time.
Particle of different masses falls with same acceleration, which is acceleration due to gravity on earth.
To change the state (state of rest or state of motion) of a body we need external force. Force = mass x acceleration
Hence more force will be required for heavier body.
Question 2
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A bullet of mass $$10\ g$$ moving with the velocity of $$1.5\ ms^{-1}$$ hits a thick wooden plank of mass $$90\ g$$. The plank is initially at rest, but when it gets hit by the bullet, the bullet remains in the plank, and both move with a certain speed. Calculate the speed with which the plank containing the bullet moves?

A
$$0.15\ ms^{-1}$$

B
$$0.5\ ms^{-1}$$

C
$$1.5\ ms^{-1}$$

D
$$2\ ms^{-1}$$

Solution

Mass of the bullet, $$m = 10\ gm = 0.01\ kg$$

Velocity of bullet , $$v = 1.5\ ms^{-1}$$

Mass of plank, $$m_{p} = 90\ gm = 0.09\ kg$$

Initial velocity of plank $$= 0 m/s$$

Momentum of the bullet, $$p = mv = 0.01 \times 1.5 = 0.015\ kg m/s$$

Total mass of the plank $$= m + m_{p} = 0.01 +0.09 = 0.1\ kg$$

The plank and the bullet both move with the same speed

The momentum of the plank and the embedded bullet is $$0.015\ kg m/s$$
($$\because $$ the momentum is conserved in a collision.)

But the momentum of the plank and the embedded bullet = product of their mass and velocity.

$$\therefore 0.015 = 0.1 \times v $$

$$\Rightarrow \therefore v = \dfrac{0.015}{0.1} = 0.15 m/s$$

The speed of the plank containing the bullet is $$0.15 m/s$$
Question 3
1 / -0

When a net force acts on an object, the object will be accelerated in the direction of the force with an acceleration proportional to

A
the force on the object

B
the velocity of the object

C
the mass of the object

D
the inertia of the object

Solution

According to Newton's second laws of motion the external force acting on a body is directly proportional to the rate of change of linear momentum.
i.e $$\displaystyle F \propto \frac{dp}{dt}$$ or
$$F = ma $$
$$\therefore a \propto F$$
Question 4
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A large truck and a car, both moving with a velocity of magnitude $$v$$, have a head-on collision. If the collision lasts for $$1\ s$$. Which vehicle experiences greater acceleration?

A
Car

B
Truck

C
Both have equal acceleration

D
Cannot say

Solution

Let the mass of truck $$=M$$, the mass of car$$=m$$

The velocity of truck$$=v$$;

The velocity of car $$=-v$$, (Negative sign for the opposite direction of motion).

The time for which collision lasts, $$t=1 \ s$$

Since acceleration $$a =\dfrac{force}{mass}$$,

Since, force of impact is same,

Hence, acceleration $$a\propto \dfrac {1}{mass}$$.

As the mass of the car is smaller, therefore the acceleration produced in the car is greater than the acceleration of the truck.
Question 5
1 / -0

Suppose you push a spring with a force $$F_1$$ as shown in figure, the spring also pushes up on your hand with a force $$F_2$$. What is the relationship between $$F_1$$ and $$F_2$$?

A
$$F_1 > F_2$$

B
$$F_1 = 2F_2$$

C
$$F_1 < F_2$$

D
$$F_1 = F_2$$

Solution

According to third law of motion: For every action, there is an equal and opposite reaction. So, when you push a spring with a force $${F}_{1}$$, the spring also pushes up on your hand with a force $${F}_{2}$$ of having same magnitude but in opposite direction hence,$${F}_{1}={F}_{2}$$
Question 6
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A large truck and a car, both moving with a velocity of magnitude $$v$$, have a head-on collision. If the collision lasts for $$1\ s$$ which vehicle experiences greater force of impact?

A
Truck

B
Car

C
Both experience equal and opposite force

D
Data insufficient

Solution

Let, mass of truck$$=M$$
Mass of car$$=m$$
Velocity of truck$$=v$$
Time for which collision lasts, t$$=1s$$
Velocity of car $$= -v$$
(Negative sign for opposite direction of motion).

According to third law of motion,on collision, both the vehicles experience the same force, as action and reaction are equal.
Question 7
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Two small glass spheres of masses 10 g and 20 g are moving in a straight line in the same direction with velocities of $$3 ms^{-1}$$ and $$2 ms^{-1}$$ respectively. They collide with each other. After collision, glass sphere of mass 10 g moves with a velocity of $$2.5 ms^{-1}$$. Find the velocity of the second ball after collision.

A
$$2.25 ms^{-1}$$

B
$$5.5 ms^{-1}$$

C
$$2.75 ms^{-1}$$

D
$$7.5 ms^{-1}$$

Solution

Here, $$m_1=10g=\dfrac {10}{1000}=0.01 kg$$

$$m_2=20 g=0.02 kg$$

$$u_1=3 ms^{-1}; u_2=2 ms^{-1}$$

$$v_1=2.5 ms^{-1}; v_2=?$$

Total momentum of both the spheres before collision $$=m_1u_1+m_2u_2$$

$$=0.01\times 3+0.02\times 2=0.07 kg ms^{-1}$$

Total momentum of both the spheres after collision

$$=m_1v_1+m_2v_2$$

$$=0.01\times 2.5+0.02v_2=0.025+0.02v_2$$

Now, according to the law of conservation of momentum,

Total momentum after collision $$=$$Total momentum before collision

$$\therefore 0.025+0.02v_2=0.07$$

or $$0.02v_2=0.07-0.025=0.045$$

or $$v_2=\dfrac {0.045}{0.02}=2.25 ms^{-1}$$
Question 8
1 / -0

The earth and the moon are attracted to each other by gravitational force. Is the force with which the Earth attracts the Moon greater, smaller or the same as the force with which the Moon attracts the Earth?

A
Same and opposite

B
Greater

C
Smaller

D
Data insufficient

Solution

Gravitation force between two bodies is equal in magnitude but opposite in direction
$$ F= \dfrac{Gm_e m_m}{r^2}$$
$$F_{em}=-F_{me}$$
$$F_{em}\rightarrow Force \ on \ earth \ due \ to \ moon$$
$$F_{me}\rightarrow Force \ on \ moon \ due \ to \ earth$$
Hence, Earth and Moon will be attracted to each other with a force equal in magnitude but opposite in direction.
Question 9
1 / -0

In which of the following cases the net force is not equal to zero?

A
A kite skillfully held stationary in the sky

B
A ball falling freely from a height

C
A helicopter hovering above the ground

D
A cork floating on the surface of water

Solution

According to newton's 1st law of motion, A body maintains its states ie Rest or motion with uniform velocity until and unless there is no external force apply on that.
So, A kite skillfully held stationary in the sky, A helicopter hovering above the ground, A cork floating on the surface of water, All these examples are maintaining state of rest so resultant or net force on it will be zero.
A freely falling ball have acceleration that will equal to $$g$$ So, Net force on it will not be equal to zero.
Question 10
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Student A and student B sit in identical office chairs facing each other, as shown in figure. Student A is heavier than student B. Student A suddenly pushes with his feet. Which of the following occurs?

A
Neither student applies a force on each other

B
A exerts a force that is applied to B, but A experiences no force

C
Each student applies a force to the other, but A exerts the larger force

D
The students exert the same amount of force on each other

Solution

Newtons third law states that all forces exist in pairs: if one object A exerts a force $${F}_{A}$$ on a second object B, then B simultaneously exerts a force $${F}_{B}$$ on A, and the two forces are equal and opposite: $${F}_{A}$$$$=$$- $${F}_{B}$$
So,the students exert same amount of force on each other in opposite direction.

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Forces and Laws of Motion Test - 43

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Forces and Laws of Motion Test - 43

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Question 1

(b) and (c)

(a) and (b)

(a), (b) and (d)

All of the above

Solution

Question 2

$$0.15\ ms^{-1}$$

$$0.5\ ms^{-1}$$

$$1.5\ ms^{-1}$$

$$2\ ms^{-1}$$

Solution

Question 3

the force on the object

the velocity of the object

the mass of the object

the inertia of the object

Solution

Question 4

Car

Truck

Both have equal acceleration

Cannot say

Solution

Question 5

$$F_1 > F_2$$

$$F_1 = 2F_2$$

$$F_1 < F_2$$

$$F_1 = F_2$$

Solution

Question 6

Truck

Car

Both experience equal and opposite force

Data insufficient

Solution

Question 7

$$2.25 ms^{-1}$$

$$5.5 ms^{-1}$$

$$2.75 ms^{-1}$$

$$7.5 ms^{-1}$$

Solution

Question 8

Same and opposite

Greater

Smaller

Data insufficient

Solution

Question 9

A kite skillfully held stationary in the sky

A ball falling freely from a height

A helicopter hovering above the ground

A cork floating on the surface of water

Solution

Question 10

Neither student applies a force on each other

A exerts a force that is applied to B, but A experiences no force

Each student applies a force to the other, but A exerts the larger force

The students exert the same amount of force on each other

Solution

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