Answer:
Explanation:
Moment of inertia of the metal rod pivoted in the middle
= M l² / 12
If the spring is compressed by small distance x twisting the rod by angle θ
restoring force by spring
= k x
moment of torque about axis
= k x l /2
= k θ( l /2 )² ( x / .5 l = θ )
=
moment of torque = moment of inertia of rod x angular acceleration
k θ( l /2 )² = M l² / 12 d²θ/dt²
d²θ/dt² = 3 k/M θ
acceleration = ω² θ
ω² = 3 k/M
ω = √ 3 k / M
E. Galaxy Cluster
Explanation:
A galaxy cluster, or cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by mutual gravity.
A megaparsec is a million parsecs and there are about 3.3 light years in a mega-parsec. Parsec is rather a natural distance unit for astronomers. The standard abbreviation of a mega-parsec is Mpc.
A parsec is approximately 3.09 x 1016 meters, a megaparsec is about 3.09 x 1022 meters.
Hence, 8 megaparsecs is gigantic size and that can be only of a galaxy cluster consisting of hundreds and thousands of galaxies bounded together.
Keywords: galaxies, parsec, megaparsec, galaxy cluster
Learn more about galaxy clusters and astronomical units from:
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I think the question meant to say net force on the box. Since force is a vector, the direction matters. 20N left is negated completely by the 50N right, which means the net force is 50N-20N to the right, 30N.
Answer:
E = 31.329 N/C.
Explanation:
The differential electric field 
at the center of curvature of the arc is
<em>(we have a cosine because vertical components cancel, leaving only horizontal cosine components of E. )</em>
where 
is the radius of curvature.
Now
,
where 
is the charge per unit length, and it has the value
Thus, the electric field at the center of the curvature of the arc is:
Now, we find 
and 
. To do this we ask ourselves what fraction is the arc length 3.0 of the circumference of the circle:
and this is
radians.
Therefore,
evaluating the integral, and putting in the numerical values we get:
Answer:
C. 98 J
Explanation:
The appropriate formula is ...
PE = mgh . . . . . m is mass; below, m is meters
PE = (5 kg)(9.8 m/s^2)(2 m) = 98 kg·m^2/s^2
PE = 98 J
