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Let the vector position of the object in the (x-y) plane be

The applied force is

By definition, the applied torque is

Answer:
The magnitude of the electrical force between a pair of charged particles is 4 Times as much when the particles are moved half as far apart.
This can be easily understood by Columb's law,

which state's that the amount of electrical force experienced by two charged particles is inversely proportional to the square of the distance between them.
∴ 
Now, we know the new distance is half the original distance,


The electrical force of attraction or electrostatic force of attraction between two charged particles refers to the amount of attractive or repulsive force that exists between the two charges. This can be calculated by Columb's Law.
A charged particle in physics is a particle that has an electric charge. It might be an ion, such as a molecule or atom having an excess or shortage of electrons in comparison to protons. The same charge is thought to be shared by an electron, a proton, or another primary particle.
Learn more about electrical force here
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Answer:
Abstracto
Los ácidos nucleicos y las proteínas comprenden una red de biomacromoléculas que almacenan y transmiten información que sustenta la vida de la célula. El estudio de estos mecanismos es un campo llamado biología molecular. El desarrollo de esta ciencia siempre ha ido acompañado de avances técnicos que permiten romper barreras metodológicas para probar hipótesis novedosas. Entre los métodos disponibles para los biólogos moleculares, destacan cinco: electroforesis, secuenciación, clonación, transferencia y reacción en cadena de la polimerasa. Su impacto llega a la genética, la medicina y la biotecnología. Aquí, se revisan la relevancia histórica, los fundamentos técnicos y las tendencias actuales de estos cinco métodos esenciales. La revisión pretende ser útil tanto para estudiantes como para científicos profesionales que buscan adquirir conocimientos avanzados sobre el valor de estos métodos para investigar los mecanismos moleculares que sostienen la vida.
We know that arc length (x(t)) is given with the following formula:

Where r is the radius of the barrel. We must keep in mind that as barrel rolls its radius decreases because less and less tape is left on it.
If we say that the thickness of the tape is D then with every full circle our radius shrinks by d. We can write this down mathematically:

When we plug this back into the first equation we get:

We must solve this quadratic equation.
The final solution is:

It is rather complicated solution. If we asume that the tape has no thickness we get simply: