Kinematics Question 158
Question: A frictionless wire Ab is fixed on a sphere of radius R. A very small spherical ball slips on this wire. The time taken by this ball to slip from A to b is
Options:
A) $ \frac{2\sqrt{gR}}{g\cos \theta } $
B) $ 2\sqrt[{}]{gR,} $
$ \frac{\cos \theta }{2} $
C) $ \sqrt[2]{\frac{R}{g}} $
D) $ \frac{gR}{\sqrt{g\cos \theta }} $
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Answer:
Correct Answer: C
Solution:
[c] Acceleration of body along Ab is distance travelled in time t sec=AB= $ \frac{1}{2} $
$ (gcos\theta )t^{2} $ From $ \Delta ABC $ , AB = $ 2R\cos \theta ;2R\cos \theta =\frac{1}{2}g\cos \theta t^{2} $
$ \Rightarrow t^{2}=\frac{4R}{8} $ or $ t=2\sqrt{\frac{R}{g}} $
