question_answer

A small particle of mass m is released from rest from point A inside a smooth hemispherical bowl as shown in the figure. The ratio (x) of magnitude of centripetal force and normal reaction on the particle at any point B varies with 9 as

A) (a)                                         

B)

C)                                                              

D)

Correct Answer: A

Solution :

 \[y(x,t)=(0.02m)\sin [(2\pi {{m}^{-1}})x+(10\pi {{s}^{-1}})t]m\]\[y(x,t)=(0.02m)\cos [(10\pi {{m}^{-1}})t+(2\pi {{s}^{-1}})x]m\] \[y(x,t)=(0.02m)\sin [(2\pi {{m}^{-1}})x-(10\pi {{s}^{-1}})t]m\]Speed of the particle at point B, \[y(x,t)=(0.02m)\sin [(\pi {{m}^{-1}})x+(5\pi {{s}^{-1}})t]m\] Centripetal force, \[\frac{2l}{3}\]    ... (i) Equation of motion gives