Question

A mass rotates in a vertical circle of radius R and has a circular speed at the top. lf the radius of the circle is increased by a factor of 4, circular speed at the top will be
A) decreased by a factor of 2
B) decreased by a factor of 4
C) increased by a factor of 2
D) increased by a factor of 4

Answer 1

Answer:

c]increased by a factor of 2

Explanation:

speed of the particle at the top of the vertical circle iS

$v=\sqrt{g*R}$

given that the radius of the circle is increased by a factor of 4

then $v'=\sqrt{g*4R}$

          $=2\sqrt{g*R}$

          $v'=2v$

therefore,it is increased by a factor of 2

Answer 2

Answer:

C) increased by a factor of 2

Explanation:

Since at the top of the circulation motion weight equals to the centripetal force i.e., v=$\sqrt{gR}$

⇒v= $\sqrt{g *4R\\}$

​     =2$\sqrt{gR}$  

Therefore if we increase the radius by a factor 4, the circular speed at the top will be increased by a factor of 2.