Laws of Motion Test

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Laws of Motion Test - 39

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Weekly Quiz Competition

Question 1
1 / -0

The effect of an impulse force on the body is measured only in terms of its

A
Force

B
Moment of momentum

C
Impulse

D
None of these

Solution

The relation between the impulsive force and impulse produced by it is $$F\times t = $$ Impulse
The effect of an impulse force of the body is measured in terms of its impulse.
Question 2
1 / -0

Physical independence of force is a consequence of _____.

A
first law of motion

B
second law of motion

C
third law of motion

D
all ofthese laws

Solution
Question 3
1 / -0

A stationary ball weighing 0.25 kg acquire a speed of $$10\:m/s$$ when hit by a hockey stick. The impulse imparted to the ball is:

A
$$0.25\:N\times s$$

B
$$2.5\:N\times s$$

C
$$2\:N\times s$$

D
$$0.5\:N\times s$$

Solution

Given : $$m = 0.25$$ kg
Initial velocity of the ball $$u = 0$$ m/s
Final velocity of the ball $$v = 10$$ m/s
Impulse imparted $$I = \Delta P = mv-mu =0.25\times 10 - 0 = 2.5$$ $$N\times s$$
Question 4
1 / -0

A disc of mass 10 g is kept floating horizontally by throwing 10 marbles per second against it from below. The marbles strike the disc normally and rebound downwards with the same speed. If the mass of each marble is 5 g, the velocity with which the marbles are striking the disc is $$\displaystyle \left( g=9.8{ m }/{ { s }^{ 2 } } \right) $$

A
$$\displaystyle 0.98m/s$$

B
$$\displaystyle 9.8m/s$$

C
$$\displaystyle 1.96m/s$$

D
$$\displaystyle 19.6m/s$$

Solution

Given that:
Mass of disc,$$M=10g=0.010kg$$
Mass of each marble,$$m=5g=0.005kg$$
Suppose the number of marbles striking the disc per second=n and velocity with which marbles strike disc is v.
Then Weight of disc acting downward$$=Mg$$
Change in velocity of marbles when they rebound $$=v-(-v)=2v$$
Therefore the change in momentum of each marble when it strikes the disc=$$m * 2v=2mv$$
and total momentum imparted per second to the disc$$=2mnv $$= The force exerted by the marbles in the upward direction
The disc will remain at rest if the net force acting on it is zero provided it is initially at rest.
Therefore for the disc to remain at rest,
Weight of disc=Upward force on it
$$= Mg=2mnv$$
$$v=\dfrac{Mg}{2mn}=\dfrac{(0.010 *9.8)}{(2*0.005*10)}$$
$$=0.98 m/s$$
Question 5
1 / -0

A stationary ball weighing 0.25 kg acquires a speed of 10 m/s when hit by a hockey stick. The impulse imparted to the ball is :

A
2.5 Ns

B
2.0Ns

C
1.5 Ns

D
0.5Ns

Solution

impulse is change in momentum so initial momentum is zero and final momentum is $$2.5 Ns$$ .
so impulse is $$2.5Ns$$ which is change in momentum .
so the answer is A.
Question 6
1 / -0

A ball weighing $$10 g$$ hits a hard surface vertically with a speed of $$5 {m}/{sec}$$ and rebounds with the same speed. The ball remains in contact with the surface for $${1}/{100} sec$$. The average force exerted by the surface on the ball is

A
$$100 N$$

B
$$10 N$$

C
$$1 N$$

D
$$0.1 N$$

Solution

Given,
$$m=10g=0.01kg$$
$$v=5m/s$$
$$t=\dfrac{1}{100} sec$$
Average force, $$F_{avg}=\dfrac{2mv}{t}$$
$$F_{}=\dfrac{2\times 0.01\times 5}{1/100}=10N$$
The correct option is B.
Question 7
1 / -0

A boat at rest has two persons of unequal weights seated at either end. If they walk across the boat and interchange their positions,

A
The boat will move in the direction of walking of the lighter person

B
The boat will move in the direction of walking of the heavier person

C
The boat will not move at all

D
The boat will oscillate about a mean position and stop once the persons have moved to the new positions

E
None of these

Solution

Answer is A.
The Centre of mass of the system should be at rest because no external force is acting on the system of the boat and 2 men.
When two men interchange their position, the center of mass of 2 men will move towards the heavier man but to keep it at its original position, the boat has to move towards the lighter man.
Question 8
1 / -0

Two forces act on either side of rigid body of negligible mass suspended by string as shown in the figure. If R is the resultant force the tension of the string T = _____ gwt.

A
$$26$$

B
$$41$$

C
$$82$$

D
$$16$$

Solution

Since the rod is in equilibrium, so net force acting on the rod is zero. Thus tension in the string balances the $$32 \ gwt$$ and $$50 \ gwt$$.
$$\therefore$$ $$T = 32+50 = 82 \ gwt$$
Question 9
1 / -0

A hammer weighing $$3 kg$$, moving with a velocity of $$10 {m}/{s}$$, strikes against the head of a spike and drives it into a block of wood. If the hammer comes to rest in $$0.025 s$$, the impulse associated with the hammer will be

A
$$30 N s$$

B
$$-30 N s$$

C
$$15 N s$$

D
$$-15 N s$$

Solution

Let J be the impulse associated with the hammer
then, $$\dfrac{\Delta J}{\Delta t} = ma$$ and a =$$\dfrac{\Delta V}{\Delta t}$$

Hence, j = m$$\Delta V$$

j= 3(0 - 10) Ns = -30 Ns
Question 10
1 / -0

A rubber of mass $$200$$ g hits a wall normally with a velocity of $$\displaystyle { 10\ ms }^{ -1 }$$ and bounces back with a velocity of $$\displaystyle { 8\ ms }^{ -1 }$$. The impulse is _____ Ns.

A
$$-0.5$$

B
$$+0.5$$

C
$$-3.6$$

D
$$+3.6$$

Solution

Initial momentum   $$P_i = mu = 0.2\times (10) = 2 \ kg \ m/s$$
Final impulse   $$P_f = mv = 0.2\times (-8) = -1.6\ kg \ m/s$$
Impulse    $$I = P_f - P_i$$
$$\implies \ I = -1.6-2 = -3.6 \ N \ s$$

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Laws of Motion Test - 39

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Laws of Motion Test - 39

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SHARING IS CARING

Question 1

Force

Moment of momentum

Impulse

None of these

Solution

Question 2

first law of motion

second law of motion

third law of motion

all ofthese laws

Solution

Question 3

$$0.25\:N\times s$$

$$2.5\:N\times s$$

$$2\:N\times s$$

$$0.5\:N\times s$$

Solution

Question 4

$$\displaystyle 0.98m/s$$

$$\displaystyle 9.8m/s$$

$$\displaystyle 1.96m/s$$

$$\displaystyle 19.6m/s$$

Solution

Question 5

2.5 Ns

2.0Ns

1.5 Ns

0.5Ns

Solution

Question 6

$$100 N$$

$$10 N$$

$$1 N$$

$$0.1 N$$

Solution

Question 7

The boat will move in the direction of walking of the lighter person

The boat will move in the direction of walking of the heavier person

The boat will not move at all

The boat will oscillate about a mean position and stop once the persons have moved to the new positions

None of these

Solution

Question 8

$$26$$

$$41$$

$$82$$

$$16$$

Solution

Question 9

$$30 N s$$

$$-30 N s$$

$$15 N s$$

$$-15 N s$$

Solution

Question 10

$$-0.5$$

$$+0.5$$

$$-3.6$$

$$+3.6$$

Solution

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