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3 years ago

Set up differential equation of angular S.H.M

Physics

1 answer:

3241004551 [841]3 years ago

3 0

Answer:

${ \sf{ \omega \: is \: the \: angular \: velocity}} \\ { \sf{ \theta \: is \: the \: angular \: displacement}}$

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1. What is true about all forces?a. They are unbalanced b. They involve more than one object c. They cause objects to moved. d.

Pachacha [2.7K]

the answer is most likely D

3 0

3 years ago

A small metal ball is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal

Gemiola [76]

Answer:

Time taken, $T=2\pi \sqrt{\dfrac{l\ cos\theta}{g}}$

Explanation:

It is given that, a small metal ball is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal circle so that the thread’s trajectory describes a cone as shown in attached figure.

From the figure,

The sum of forces in y direction is :

$T\ cos\theta-mg=0$

$T=\dfrac{mg}{cos\theta}$

Sum of forces in x direction,

$T\ sin\theta=\dfrac{mv^2}{r}$

$mg\ tan\theta=\dfrac{mv^2}{r}$ .............(1)

Also, $r=l\ sin\theta$

Equation (1) becomes :

$mg\ tan\theta=\dfrac{mv^2}{l\ sin\theta}$

$v=\sqrt{gl\ tan\theta.sin\theta}$ ...............(2)

Let t is the time taken for the ball to rotate once around the axis. It is given by :

$T=\dfrac{2\pi r}{v}$

Put the value of T from equation (2) to the above expression:

$T=\dfrac{2\pi r}{\sqrt{gl\ tan\theta.sin\theta}}$

$T=\dfrac{2\pi l\ sin\theta}{\sqrt{gl\ tan\theta.sin\theta}}$

On solving above equation :

$T=2\pi \sqrt{\dfrac{l\ cos\theta}{g}}$

Hence, this is the required solution.

4 0

3 years ago

A 0.001kg bullet is fired with a velocity of 800m/s into a soft wood of mass 1kg resting on a smooth surface. Find the final vel

V125BC [204]

The final velocity of the bullet+block is 0.799 m/s

Explanation:

We can solve this problem by applying the principle of conservation of momentum: in fact, the total momentum of the bullet-block system must be conserved before and after the collision.

Mathematically, we can write:

$mu+MU=(m+M)v$