Tag: laws of motion

Quizzes (7) Questions (14)

Questions Related to laws of motion

Multiple choice friction laws of motion physics

A block released from rest from the top of a smooth inclined plane of angle $\theta _1$ reaches the bottom in time $t _1$. The same block released from rest from the top of another smooth inclined plane of angle $\theta _2$, reaches the bottom in time $t _2$. If the two inclined planes have the same height, the relation between $t _1$ and $t _2$ is 

  1. $\cfrac{t _2}{t _1} = \left(\cfrac{sin \theta _1}{sin \theta _2}\right)^{1/2}$

  2. $\cfrac{t _2}{t _1} = 1$

  3. $\cfrac{t _2}{t _1} = \left(\cfrac{sin \theta _1}{sin \theta _2}\right)$

  4. $\cfrac{t _2}{t _1} = \left(\cfrac{sin^2 \theta _1}{sin^2 \theta _2}\right)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
From the figure
we see that
down the incline acceleration us $a=g\sin \theta$
distance $s=\dfrac {h}{\sin \theta _1}$

using $s=ut+\dfrac {1}{2} at^2 \ ;\ u=0$ (initially rest)

gives $t=\sqrt {\dfrac {2s}{a}}$

For $\theta _1 \quad t _1=\sqrt {\dfrac {2\ h}{\sin \theta _1 \times g\sin \theta _1}}=\dfrac {1}{\sin \theta _1} \sqrt {\dfrac {2\ h}{g}}$

so for $O _2, \ t _2=\dfrac {1}{\sin \theta _2}\sqrt {\dfrac {2\ h}{g}}$

$\Rightarrow \ \dfrac {t _2}{t _1}=\dfrac {\sin \theta _1}{\sin \theta _2}$
Multiple choice friction laws of motion physics

A coin placed on a rotating turn table just slips if it is at a distance of $40\  cm$ from the centre if the angular velocity of the turntable is doubled, it will just slip at a distance of:

  1. $10\ cm$

  2. $20\ cm$

  3. $40\ cm$

  4. $80\ cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

It slips when.
$\mu mg = m{\omega ^2}r$
$ \Rightarrow \mu g = {\omega ^2}r$
$ \Rightarrow \mu g = {\omega ^2}40 - \left( 1 \right)$
$Now,\,\omega  = 2\omega $
$ \Rightarrow \mu g = {\left( {2\omega } \right)^2}r \Rightarrow 4{\omega ^2}r - \left( 2 \right)$
$\therefore {\omega ^2} \times 40 = 4{\omega ^2}r$
$ \Rightarrow r = 10cm$

Multiple choice friction laws of motion physics

The coefficient of friction between two surfaces is 0.2. The angle of friction is 

  1. sin$^{-1}$(0.2)

  2. cos $^{-1}$(0.2)

  3. tan$^{-1}$(0.1)

  4. cot$^{-1}$(5)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
The correct option is D

We have,

 The coefficient of friction is $0.2$

Since we know that,

The coefficient of friction $= tan \theta$  Where $\theta $  is the angle of friction.

$\dfrac{1}{5}=tan \theta$

$\theta=tan^{-1}\dfrac{1}{5}$

$=cot^{-1}5$
Multiple choice friction laws of motion physics

If angle of repose is ${30}^{o}$, then coefficient of friction will be

  1. $1$

  2. $15$

  3. $\cfrac { 1 }{ \sqrt { 3 } } $

  4. $\cfrac { \sqrt { 3 } }{ 2 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\mu =tan\theta \ =tan30=\frac { 1 }{ \sqrt { 3 }  } \ $


Multiple choice friction laws of motion physics

The coefficient of friction between a chain & a table is m. If a chain is placed on a horizontal table so that a part of it is hanging from one end, the minimum fraction of length of the chain that can be on the table, so that the chain may not slip off is

  1. $\frac{\mu}{\mu + 1}$

  2. $\frac{1}{\mu + 1}$

  3. 1

  4. Zero
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For the chain not to slip, the friction force on the table portion must equal the weight of the hanging portion. If L is the total length and x is the length on the table, then mu * (x/L) * m * g = ((L-x)/L) * m * g. Solving for the fraction x/L gives mu/(mu+1).

Multiple choice friction laws of motion physics

A piece of wood of mass $150$ g rests on an inclined plane. The co-efficient of friction between the surfaces in contact is $0.3$. To what maximum extent the plane may be inclined without allowing the piece to clip down?

  1. <span>$26.7^o$.</span>

  2. <span>$16.7^o$.</span>

  3. <span>$36.7^o$.</span>

  4. <span>$46.7^o$.</span>
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The maximum angle of inclination before sliding occurs is given by tan(theta) = mu. With mu = 0.3, theta = arctan(0.3), which is approximately 16.7 degrees.

Multiple choice friction laws of motion physics

A solid cylinder is placed on a rough inclined surface of inclination $\theta$. Minimum value of coefficient of static friction between the cylinder and the surface so that the cylinder rolls without slipping is

  1. $\dfrac{1}{3}tan\theta$

  2. $\dfrac{1}{3}sin\theta$

  3. $\dfrac{2}{3}tan\theta$

  4. $\dfrac{2}{3}sin\theta$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a solid cylinder to roll without slipping on an incline, the friction force f = (1/3)mg*sin(theta). The condition f <= mu*N = mu*mg*cos(theta) leads to mu >= (1/3)tan(theta).

Multiple choice friction laws of motion physics

The upper half of an inclined plane with inclination $\alpha $ is perfectly smooth while the lower half is rough, a body starts from rest at the top of the inclined and comes to rest again at the bottom of it. The coefficient of friction for the lower half of the incline is:

  1. $\frac { 1 }{ 2 } tan\alpha $

  2. $2sin\alpha $

  3. $cot\alpha $

  4. $2tan\alpha $
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice friction laws of motion physics

A block is kept on a horizontal table. The table is undergoing simple harmonic motion of frequency $3\, Hz$ in a horizontal plane. The coefficient of static friction between the block and the table surface is $0.72$. Find the maximum amplitude of the table at which the block does not slip on the surface $(g = 10\, ms^{-2})$

  1. $0.01m$

  2. $0.02m$

  3. $0.03m$

  4. $0.04m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The maximum acceleration of the table is a_max = omega^2 * A = (2*pi*f)^2 * A. For the block not to slip, a_max <= mu*g. Substituting f=3, mu=0.72, and g=10, we get (2*pi*3)^2 * A <= 7.2. Solving for A gives 7.2 / (36 * pi^2) approx 0.02m.

Multiple choice friction laws of motion physics

A lineman of mass 60 kg is holding a vertical pole. The coefficient of static friction between his hands and the pole is 0.5.If the able to climb up the pole,Then the minimum force with which he should press the pole with his hands $ [g = 10 ms^{-2}] is $

  1. 1200 N

  2. 600 N

  3. 300 N

  4. 150 N
Reveal answer Fill a bubble to check yourself
C Correct answer