Ratios and proportional reasoning Knowledge-Based Download PDF

Questions

1. 1.

   The electrical resistance of a uniform wire is given by $R = \rho \frac{L}{A}$, where $L$ is the length and $A$ is the cross-sectional area. If the length of the wire is tripled and its cross-sectional area is reduced to one-half of its original value, what is the new resistance in terms of $R$?

   • A) $\frac{3}{2}R$
   • B) $3R$
   • C) $6R$
   • D) $\frac{2}{3}R$
2. 2.

   Two solid spheres made of the same uniform material have radii $r$ and $3r$. If the sphere of radius $r$ has a mass of $M$, what is the mass of the sphere of radius $3r$ in terms of $M$?

   • A) $3M$
   • B) $9M$
   • C) $27M$
   • D) $81M$
3. 3.

   The magnitude of the gravitational force between two particles separated by a distance $r$ is $F$. If the distance between the particles is increased to $3r$ while their masses remain unchanged, what is the new gravitational force in terms of $F$?

   • A) $9F$
   • B) $3F$
   • C) $\frac{1}{3}F$
   • D) $\frac{1}{9}F$
4. 4.

   A particle of mass $m$ moving at speed $v$ has a kinetic energy $K$. If the mass of the particle is doubled and its speed is tripled, what is its new kinetic energy in terms of $K$?

   • A) $6K$
   • B) $12K$
   • C) $18K$
   • D) $36K$