Forces and Laws of Motion Test

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Forces and Laws of Motion Test - 37

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Weekly Quiz Competition

Question 1
1 / -0

When two identical balls are moving with equal speeds in opposite directions, which of the following is true for the system of two bodies?

A
Momentum is zero, kinetic energy is zero

B
Momentum is not zero, kinetic energy is zero

C
Momentum is zero, kinetic energy not zero

D
Momentum is not zero, kinetic energy is not zero

Solution

Let mass of the balls be $$m_1$$ and $$m_2$$ and their velocities $$v_1$$ and $$v_2$$ respectively.
$$m_1 = m_2 ,\ v_1 = -v_2$$
Total momentum,
$$\vec{p}_{total} = m_1 \vec{v_1} + m_2 \vec{u_2}$$
$$\vec{p}_{total} = m_1 \vec{v_1} - m_1 \vec{v_1} = 0$$

Total kinetic energy,
$$E = \dfrac{1}{2} m_1 v^2_1 + \dfrac{1}{2} m_2 v_2^2$$

$$E = \dfrac{1}{2} m_1 v^2_1 + \dfrac{1}{2} m_1 v^2_1 = m_1v^2_1$$
So momentum is zero, kinetic energy is not zero.
Question 2
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A ball of mass $$0.2 \ kg$$ is thrown vertically upwards by applying a force by hand. If the hand moves $$0.2 \ m$$ while applying the force and the ball goes upto $$2 \ m$$ height further, find the magnitude of force applied by the hand. Consider $$g =10$$ $${ ms }^{ -2 }$$.

A
$$20 \ N$$

B
$$22 \ N$$

C
$$4 \ N$$

D
$$16 \ N$$

Solution

The height attained by the ball $$h=2 \ m$$
So, the velocity of ball when leaving the hand $$=\sqrt{2gh}=\sqrt{40} \ m/s$$

By using 3rd equation of motion for the duration while the force was applied,
$$v^{2}-u^{2}=2as$$
$$40=2\times a\times 0.2$$
$$a=100m/s^{2}$$

By Newton's second law of motion,
$$F _{net}$$ = Mass of ball $$\times$$ acceleration $$=20$$ N in upward direction
$$F _{net} = F _{hand} - F _{gravity}$$
$$F_{hand}$$ = $$20 + mg = 20+(0.2\times 10)$$
$$F_{hand}=22 \ N$$
Question 3
1 / -0

When you are holding a ball in your hand, the reaction force to the force of gravity on the ball is, the force exerted by the:

A
ball on the earth.

B
ball on the hand.

C
hand on the ball.

D
earth on the ball.

Solution

According to the newton's third law of motion, when the earth exerts gravitational force on the ball, the ball also exerts an equal and opposite force on earth.
Question 4
1 / -0

If a net force $$F$$ applied to an object of mass $$m$$ will produce an acceleration of $$a$$, what is the mass of a second object which accelerates at $$5a$$ when acted upon by a net force of $$2F$$?

A
$$\dfrac{2}{5}m$$

B
$$2m$$

C
$$\dfrac{5}{2} m$$

D
$$5m$$

Solution

According to Newton's second law $$F=ma$$.

For first object
$$F=m\times a$$ ...........(1)

For second object
and $$2F=m'\times5a$$..........(2)

Solving these two equations, we get
$$\Longrightarrow\ 2m \times a=m' \times 5a $$
$$ \Longrightarrow m_2=\dfrac{2m}{5} $$
Option A
Question 5
1 / -0

A block weighing $$30 \ N$$ is on a smooth horizontal surface and it is accelerated in the horizontal direction at a rate of $${4 \ m/s}^{ 2 }$$ by a force. The net force in horizontal direction acting on the block is (g $$={ 10 m/s }^{ 2 }$$ ):

A
12 N

B
120 N

C
50 N

D
10 N

Solution

Weight of the block $$W=mg$$
N is the normal reaction acting on the block due to the horizontal surface (mg is downward and N is upward)
So $$N=mg$$ as there is no acceleration in vertical direction.

The net force experienced by the block will be in the horizontal direction and will be equal to the product of mass and acceleration.
Mass: $$m=\dfrac{W}{g}=\dfrac{30 \ N}{10 \ m/s^2} = 3 kg$$

Hence, by Newton's second law of motion,
Force $$F=ma = 3 \ kg \times 4 \ m/s^2 = 12 \ N$$
Question 6
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A body of mass $$2 \ kg$$ moving on a horizontal surface with an initial velocity of $$4 \ ms^{-1}$$, comes to rest after $$2 \ s$$. If one wants to keep this body moving on the same surface with a velocity of $$4ms^{-1}$$, the force required is:

A
zero

B
$$2 \ N$$

C
$$4 \ N$$

D
$$8 \ N$$

Solution

Given:
Mass $$m = 2 \ kg$$
Initial velocity $$u=4 \ ms^{-1}$$
Final velocity $$v=0$$
Time $$t=2 \ s$$

The body comes to rest due to a retarding acceleration provided by a force, say $$F_1$$.

Let us calculate this acceleration by first equation of motion.
$$v=u+at$$
$$\Rightarrow 0=4+a(2)$$
$$\Rightarrow a= \dfrac{-4}{2}=-2 \ m/s^2$$

By Newton's second law, the force providing this acceleration must be
$$F_1=mass \times acceleration$$
$$\Rightarrow F_1=2 \times -2=-4N$$
Negative sign indicates the force is opposite to the velocity.

Now, to keep the body moving with the same velocity, the net force on the body must be zero. The force $$F_2$$ required to do so must be equal and opposite to $$F_1.$$
$$F_2=-(F_1)=-(-4 \ N)=+4 \ N$$

Option (C) is correct.
Question 7
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Inside a railway car a plumb bob (a heavy mass suspended by a thread) is suspended from the roof and a helium filled balloon is tied by a string to the floor of the car. When the railway car accelerates to the right, then

A
Both the plumb bob and balloon move to the left

B
Both the plumb bob and balloon move to the right

C
Plumb bob moves to the left and the balloon moves to the right

D
Plumb bob moves to the right and the balloon moves to the left

Solution

The bob due to its inertia tries to be in its original state. So, when the car starts, it tries to resist the motion and tries to maintain its position and so it moves to the left when the car moves to the right.
But the case of the balloon is different. Balloon, being lighter than air, floats in the air. So, when the car is accelerated, the air, due to its inertia moves left which increases the pressure there and hence the balloon moves at the right.
Question 8
1 / -0

A father and his seven year old son are facing each other on ice skates (assume no friction with the ground). With their hands, they push off against one another. Regarding the forces that act on them as a result of this and the accelerations they experience. Which of the following statements is correct?

A
Father exerts more force on the son and experiences less acceleration.

B
Son exerts less force on the father and experiences more acceleration.

C
Father exerts as much force on the son as the son exerts on the father, but the father experiences less acceleration.

D
Father exerts as much force on the son as the son exerts on the father, but the father experiences more acceleration.

Solution

The normal forces between the father and son constitute an action-reaction pair. Therefore they are equal.
But since the mass of father is greater compared to son, the acceleration of father is lesser than the son.
Acceleration of son : $$a_{son} : \frac{F}{m}$$
Acceleration of father : $$a_{father} : \frac{F}{M}$$
As m<M hence $$a_{son}>a_{father}$$
Question 9
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A person weighing 60 kg in a small boat of mass 140 kg that is at rest, throws a 5 kg stone in the horizontal direction with a velocity of $$14ms^{-1}$$ . The magnitude of velocity of the boat immediately after the throw is:

A
$$1.2 ms^{-1}$$

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

C
$$0.35 ms^{-1}$$

D
$$0.65 ms^{-1}$$

Solution

As there is no external force applied, momentum of system will remain conserved.
Initial momentum $$=$$ final momentum
$$\Rightarrow$$ $$(5)(14) = (140+60)(V)$$, finally system (boat + person) will move with velocity $$V$$.
This gives $$V = 0.35 m/s.$$
Question 10
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A bullet of mass $$10\ g$$ moving with a horizontal velocity $$100\ m/s$$ passes through a wooden block of mass $$100\ g$$. The block is resting on a smooth horizontal floor. After passing through the block the velocity of the bullet is $$10\ m/s$$. The velocity of the emerging bullet with respect to the block is:

A
$$10\ m/s$$

B
$$9 \ m/s$$

C
$$1 \ m/s$$

D
$$5\ m/s$$

Solution

Using momentum conservation,

$$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2 $$

$$m_1=10\ g$$ $$,m_2=100\ g$$ $$,u_1=100\ m/s$$ $$,u_2=0$$ $$,v_1=10\ m/s$$

$$\Rightarrow 10\times 100+100 \times 0= 10 \times 10+100\times v_2$$

$$\Rightarrow 1000 = 100 + 100v_2 \Rightarrow v_2=9\ m/s $$

Therefore $$v_1$$ with respect to $$v_2 =v_1-v_2=1\ m/s$$

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Re-Attempt Weekly Quiz Competition

Forces and Laws of Motion Test - 37

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Forces and Laws of Motion Test - 37

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Question 1

Momentum is zero, kinetic energy is zero

Momentum is not zero, kinetic energy is zero

Momentum is zero, kinetic energy not zero

Momentum is not zero, kinetic energy is not zero

Solution

Question 2

$$20 \ N$$

$$22 \ N$$

$$4 \ N$$

$$16 \ N$$

Solution

Question 3

ball on the earth.

ball on the hand.

hand on the ball.

earth on the ball.

Solution

Question 4

$$\dfrac{2}{5}m$$

$$2m$$

$$\dfrac{5}{2} m$$

$$5m$$

Solution

Question 5

12 N

120 N

50 N

10 N

Solution

Question 6

zero

$$2 \ N$$

$$4 \ N$$

$$8 \ N$$

Solution

Question 7

Both the plumb bob and balloon move to the left

Both the plumb bob and balloon move to the right

Plumb bob moves to the left and the balloon moves to the right

Plumb bob moves to the right and the balloon moves to the left

Solution

Question 8

Father exerts more force on the son and experiences less acceleration.

Son exerts less force on the father and experiences more acceleration.

Father exerts as much force on the son as the son exerts on the father, but the father experiences less acceleration.

Father exerts as much force on the son as the son exerts on the father, but the father experiences more acceleration.

Solution

Question 9

$$1.2 ms^{-1}$$

$$0.5 ms^{-1}$$

$$0.35 ms^{-1}$$

$$0.65 ms^{-1}$$

Solution

Question 10

$$10\ m/s$$

$$9 \ m/s$$

$$1 \ m/s$$

$$5\ m/s$$

Solution

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