Laws of Motion Test

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Laws of Motion Test - 25

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Question 1
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A simple pendulum, composed of a bob of mass $$m$$ connected to the end of a massless rod, executes simple harmonic motion as it swings through small angles of oscillation.The maximum angular displacement with the vertical is denoted by $${ \theta }_{ max }$$. Frictional effects and variation of acceleration due to gravity are negligible.
Find out the correct statement?

A
At $$\theta=0$$, the tangential acceleration is $$0$$

B
At $$\theta={\theta}_{max}$$, the tangential acceleration is $$0$$

C
At $$\theta=0$$, the speed is $$0$$

D
At $$\theta=0$$, the restoring force is maximized

E
At $$\theta={\theta}_{max}$$, the speed is maximized

Solution

We know the tangential acceleration in SHM is given by
$$a=-{\omega}^{2}A\sin{\theta}$$
where $$A=amplitude$$
therefore at $$\theta=0$$
$$a=-{\omega}^{2}A\sin{0^0}$$
or $$a=0$$ because $$\sin{0^0}=0$$
Question 2
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A physics student is performing a experiment in which she twirls rubber stopper at the end of a string around in a circle at nearly constant speed and tries to determine its acceleration. Which of the following single changes would enables her to most nearly double the acceleration of the rubber stopper?

A
Double the speed of the rubber stopper.

B
Use a string that is twice as long as the original string.

C
Reduce the speed of the rubber stopper to half its original value.

D
Use a string that is half as long as the original string

E
Use a rubber stopper with twice as much mass as the original rubber stopper.

Solution

Due to constant speed , student is doing uniform circular motion so tangential acceleration is zero .
as the tangential acceleration is zero , therefore total acceleration will be equal to centripetal acceleration , which is
$$a=v^{2}/r$$
which can be doubled by using a string that is half as long as the original string .
$$a'=\dfrac{v^{2}}{\frac{r}{2}}=2a$$
Question 3
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Which of the following statements is NOT true?

A
When the mass of a body is doubled, the momentum of a body is halved, provided the velocity remains the same.

B
The pain we feel in the hand on hitting the wall is a consequence of Newton's third law of motion.

C
A table-cloth which is pulled from a table without dislodging the dishes is due to inertia of rest.

D
Momentum is a vector quantity.

Solution

The momentum of a body is a product of mass and its velocity. ie $$\vec P=m\ \vec v$$ it is a vector quantity.
hence when the mass of body is doubled by keeping its velocity constant then momentum of body will be double.
hence Statement $$a$$ is wrong and statment $$d$$ is right.
According to statement given in $$b$$ is correct because according to newton's 3rd law; every action have equal and opposite reaction therefore when you will hit the wall by a force (action force), with same force wall will hit your hand (Reaction force) hence hand feel pain.
Statment $$c$$ can be explained by the properties of inertia of rest. When you pull the table cloth quickly then external force will not transfer to the dishes so it wil stay in rest.
Question 4
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Which of the following physical quantities has the same units as that of impulse?

A
Momentum

B
Force

C
Torque

D
Couple

Solution

Impulse is equal to change in momentum, so both of them have same units.
Question 5
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A ball of mass $$m$$ is attached with the string of length $$R$$, rotating in a circular motion, with instantaneous velocity $$v$$ and centripetal acceleration $$a$$.
Calculate the centripetal acceleration of the ball if its mass is doubled?

A
$${a}/{4}$$

B
$${a}/{2}$$

C
$$a$$

D
$$2a$$

E
$$4a$$

Solution

As centripetal acceleration is given by $$a=v^{2}/R$$
therefore centripetal acceleration does not depend upon mass of ball, so it will remain constant ,equal to $$a$$.
Question 6
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A man in a minivan rounds a circular turn at a constant speed. Which of the following would cause the minivan to experience less acceleration ?

A
traveling faster

B
traveling around a turn with a smaller circular radius

C
traveling with more weight in the van

D
traveling around a turn with a greater circular radius

E
traveling the opposite direction around the same turn

Solution

$$a=\frac { { v }^{ 2 } }{ R } $$. So for the lesser acceleration the speed of the car should be less and the radius of curvature must be large. Correct answer is option D
Question 7
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A simple pendulum, composed of a bob of mass $$m$$ connected to the end of a massless rod, executes simple harmonic motion as it swings through small angles of oscillation.The maximum angular displacement with the vertical is denoted by $${ \theta }_{ max }$$. Frictional effects and variation of acceleration due to gravity are negligible.
Which one of the following would enable you to calculate the length of the pendulum?

A
The mass of the bob

B
The period of the oscillations

C
The tangential acceleration at $$\theta = 0$$

D
The maximum speed of the bob

E
The acceleration at $$\theta = {\theta}_{max}$$

Solution

For the small oscillation, the motion of the pendulum can be treat as a simple harmonic motion. So, time period of a SHM is $$T=2\pi\sqrt{\frac{l}{g}}$$
Thus, time period would enable you to calculate the length of the pendulum.
Question 8
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Which of the following balls is easier to catch even though all of them are moving with the same velocity?

A
Tennis ball

B
Cricket ball

C
Basket ball

D
Both cricket and basket ball

Solution

Tennis ball is lighter in weight as compare to cricket ball and thus has momentum much less than the momentum of cricket ball and basket ball ( momentum is equal to mass × velocity)
body that has large momentum possesses large impact as well thus cricket ball,basket ball having more momentum than tennis ball even if they move with same velocities causes more impact on the hands of person that tends to catch it and might sometimes get hurt thus it is easy to catch a tennis ball because its momentum is less so is its impact
Question 9
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To reduce the momentum of a given body to half its original value, its velocity must be ___________.

A
reduced to half

B
doubled

C
quadrupled

D
kept unchanged

Solution

The momentum of a body is given by
$$=MV$$
where M is mass and V is velocity
$$P=MV$$
So if M is constant and $${P}'=\frac{P}{2}$$
$$\frac{P}{2}=M{V}'$$
$${V}'=\frac{V}{2}$$
Question 10
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The maximum safe speed for a vehicle taking a turn on a curved banked road, does not depend upon

A
acceleration due to gravity

B
mass of the vehicle

C
angle of inclination with the horizontal

D
radius of curvature of the track

Solution

The maximum safe speed for a vehicle taking a turn on a curved banked road
is given by $$v=\sqrt{(\mu*rg)}$$
hence it doesn't depend upon the mass of vehicles

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Laws of Motion Test - 25

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Laws of Motion Test - 25

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Question 1

At $$\theta=0$$, the tangential acceleration is $$0$$

At $$\theta={\theta}_{max}$$, the tangential acceleration is $$0$$

At $$\theta=0$$, the speed is $$0$$

At $$\theta=0$$, the restoring force is maximized

At $$\theta={\theta}_{max}$$, the speed is maximized

Solution

Question 2

Double the speed of the rubber stopper.

Use a string that is twice as long as the original string.

Reduce the speed of the rubber stopper to half its original value.

Use a string that is half as long as the original string

Use a rubber stopper with twice as much mass as the original rubber stopper.

Solution

Question 3

When the mass of a body is doubled, the momentum of a body is halved, provided the velocity remains the same.

The pain we feel in the hand on hitting the wall is a consequence of Newton's third law of motion.

A table-cloth which is pulled from a table without dislodging the dishes is due to inertia of rest.

Momentum is a vector quantity.

Solution

Question 4

Momentum

Force

Torque

Couple

Solution

Question 5

$${a}/{4}$$

$${a}/{2}$$

$$a$$

$$2a$$

$$4a$$

Solution

Question 6

traveling faster

traveling around a turn with a smaller circular radius

traveling with more weight in the van

traveling around a turn with a greater circular radius

traveling the opposite direction around the same turn

Solution

Question 7

The mass of the bob

The period of the oscillations

The tangential acceleration at $$\theta = 0$$

The maximum speed of the bob

The acceleration at $$\theta = {\theta}_{max}$$

Solution

Question 8

Tennis ball

Cricket ball

Basket ball

Both cricket and basket ball

Solution

Question 9

reduced to half

doubled

quadrupled

kept unchanged

Solution

Question 10

acceleration due to gravity

mass of the vehicle

angle of inclination with the horizontal

radius of curvature of the track

Solution

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