question_answer

Two stones of masses m and 2 m are whirled in horizontal circles, the heavier one in a radius \[\frac{r}{2}\] and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value n is                                    [NEET 2015 (Re)]

A) 2

B) 3                     

C) 4

D) 1

Correct Answer: A

Solution :

Given, that two stones of masses m and 2 m are whirled in horizontal circles, the heavier one in a radius \[\frac{r}{2}\] and lighter one in radius r as shown in figure.

As, lighter stone is n times that of the value of heavier stone when they experience same centripetal forces, we get

\[{{({{F}_{c}})}_{heavier}}={{({{F}_{c}})}_{lighter}}\]

\[\Rightarrow \]   \[\frac{2m{{(v)}^{2}}}{(r/2)}=\frac{m{{(nv)}^{2}}}{r}\]

\[\Rightarrow \]   \[{{n}^{2}}=4\]

\[\Rightarrow \]   \[n=2\]