Tag: angular simple harmonic motion

Question 1

A large box is accelerated up the inclined plane with an acceleration a and pendulum is kept vertical (Somehow by an external agent) as shown in figure.Now if the pendulum is set free to oscillate from such position, then what is the tension in the string immediately after the pendulum is set free? (mass of $500m$)

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

$mg$
$ma _{o} \sin\theta$
$\left( m g + m a _ { 0 } \sin \theta \right)$
Zero

Answer

Correct Option: C

Question 2

The time period of oscillation of a torsional pendulum of moment of inertia I is

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

$T =2 \pi \sqrt{I/k}$
$T =2 \pi \sqrt{I/2k}$
$T =2 \pi \sqrt{2I/k}$
$T =2 \pi \sqrt{I/4k}$

Answer

Correct Option: A

Question 3

A bullet of mass $'m'$ hits a pendulum bob of mass $'2m'$ with a velocity $'v'$ and comes out of the bob with velocity $v/2$. Length of the pendulum is $2$ meter and $g=10 ms^{-2}$. The minimum value of $'v'$ for the bullet so that the bob may complete one revolution in the verticle is

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

$40 ms^{-1}$
$2.20 ms^{-1}$
$3.15 ms^{-1}$
$10 ms^{-1}$

Answer

Correct Option: A

Question 4

Time period of a disc about a tangent parallel to the diameter is same as the time period of a simple pendulum. The ratio of radius of disc to the length of pendulum is :

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

$\dfrac { 1 } { 4 }$
$\dfrac { 4 } { 5 }$
$\dfrac { 2 } { 3 }$
$\dfrac { 1 } { 2 }$

Answer

Correct Option: C

Question 5

A pendulum of mass $m$ hangs from a support fixed to a trolley. The direction of the string (i.e.., angle $\theta$) when the trolley rolls up a plane of inclination $\alpha$ with acceleration $'a'$ is

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

Zero
$\tan^{-1} \alpha$
$\tan^{-1}\dfrac{a+g \sin \alpha}{g \cos \alpha}$
$\tan^{-1}\dfrac{a}{g}$

Answer

Correct Option: C

Question 6

The oscillations of a pendulum slow down due to

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

the force exerted by air and friction at the support
the foce exerted by air only
the forces exerted by friction at the support only
none of these

Answer

Correct Option: A

Question 7

The pendulum of a certain clock has time period $2.04 s$. How fast or slow does the clock run during $24$ hour?

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

$28.8$ minutes slow
$28.8$ minutes fast
$14.4$ minutes fast
$14.4$ minutes slow

Answer

Correct Option: A

Question 8

A string of simple pendulum can bear maximum tension that is twice the weight of the bob. What is the maximum angle $(\theta)$ with which it can oscillate?

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

$0^0$
$45^0$
$60^0$
$90^0$

Answer

Correct Option: B

Question 9

A bob is suspended from an ideal string of length $l$. Now it is pulled to a side through $60^{o}$ to vertical and rotates along a horizontal circle. Then its period of revolution is

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

$ 2\pi \sqrt{ l/g }$
$ \pi \sqrt{ l/2g }$
$\pi\sqrt{ 2l/g }$
$\pi\sqrt{ l/g }$

Answer

Correct Option: C

Question 10

Two simple pendulums have time period $4\ s$ and $5\ s$ respectively. If they started simultaneously from the mean positive in the same direction, then the phase difference between them by the time the larger one completes one osicillation is

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

$\dfrac {\pi}{6}$
$\dfrac {\pi}{3}$
$\dfrac {\pi}{2}$
$\dfrac {\pi}{4}$

Answer

Correct Option: A

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