Radial & Tangential Acceleration for Non Uniform Circular Motion
Figure shows ...
Question
Figure shows a smooth vertical circular track of radius R. A block slides along the surface AB when it is given a velocity equal to √6gR at point A. The ratio of the force exerted by the track on the block at point A to that at point B is
A
0.25
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B
0.35
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C
0.45
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D
0.55
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Solution
The correct option is D0.55
Free body diagram at A and B shown is figure
Solving from block's frame of reference, we have to assume a centrifugal force of mv2R.
At point A: NA+mgcos60∘=mv2AR ⇒NA=m(√6gR)2/R−mgcos60∘=5.5mg
Using energy conservation between A and B, taking B as a reference 12mv2A+mgR(1+cos60∘)=12mv2B ⇒v2B=6gR+3gR⇒v2B=9gR
At point B, NB=mg+mv2BR ⇒NB=10mg
Therefore, NANB=5.5mg10mg=0.55