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Orlov [11]
3 years ago
6

A larger object is made of two balls separated by a massless rigid rod that is 1.5 m long. The mass of the red ball at one end i

s 1 kg and the mass of the orange ball at the other end is 5.7 kg. As in example 12.1, the balls are rotating about the center of mass. Calculate the speed of the 1 kg red ball if the angular velocity is 1 rev/s.
Physics
1 answer:
lions [1.4K]3 years ago
5 0

Answer:

The speed of the 1 kg red ball 8.04 m/s .

Explanation:

Given :

Separation between rods , d = 1.5 m .

Mass of the red ball is 1 kg .

Mass of the orange ball is 5.7 kg .

Angular velocity , \omega=1\ rev/s = 2\pi\ rad/s .

Now , distance of center of mass  from red ball is :

r =\dfrac{0\times 1+1.5\times 5.7}{1+5.7}\\\\r = 1.28\ m

We know , speed is given by :

v=\omega r\\\\v=2 \times \pi \times  1.28\\\\v=8.04\ m/s

Hence , this is the required solution .

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A stone is thrown upward from the top of a building at an angle of 30° to the horizontal and with an initial speed of 20 m/s. Th
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Answer:

Explanation:

Given

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initial speed u=20\ m/s

Point of release is 45 m above the ground

Considering stone to be a projectile, so time taken by projectile for its zero vertical displacement is

t_1=\frac{2u\sin \theta }{g}

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Now after completing zero vertical displacement , stone needs to travel another 45 m in downward direction with initial speed u=20\sin 30

h=u_yt+\frac{1}{2}a_yt^2

where, h=height

u_y=vertical velocity

a_y=vertical acceleration

t_0=time

45=20\sin 30+\frac{1}{2}(9.8)(t_0)^2

t_0^2=\frac{70}{9.8}

t_0=2.64\ s

thus total time time required is t=t_0+t_1=2.64+2=4.64\ s

vertical velocity just before hitting

v_y=\sqrt{u_y^2+2\times a_y\times s}

v_y=\sqrt{10^2+2\times 10\times 45}

v_y=\sqrt{1000}=31.622\ m/s

Horizontal velocity v_x=u\cos 30=17.32\ m/s

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=\sqrt{(17.32)^2+(31.62)^2}

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3 years ago
A rod of length L and mass M has a nonuniform mass distribution. The linear mass density (mass per length) is λ=cx2, where x is
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Answer:

Explanation:

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= ML⁻³

B )

We shall find out the mass of the rod with the help of given expression of mass per unit length and equate it with given mass that is M

The mass in the rod is symmetrically distributed on both side of middle point.

we consider a small strip of rod of length dx at x distance away from middle point

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M = ∫cx² dx

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C ) Moment of inertia of rod

∫dmx²

= ∫λdxx²

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= (c / 80) L⁵

= (12 M L⁻³/80)L⁵

= 3/20 ML²

=

=

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