question_answer

Two stones of masses m and 2m 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                                

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 \[{{({{F}_{c}})}_{\text{heavier}}}={{({{F}_{c}})}_{\text{lighter}}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\frac{2m{{(v)}^{2}}}{(r/2)}=\frac{m{{(nv)}^{2}}}{r}\] \[\Rightarrow \,\,\,\,{{n}^{2}}=4\] \[\Rightarrow \,\,\,\,\,n=2\]