First slide

Conservation of mechanical energy

Question

A ball of mass ‘m’ is rotated in a vertical circle with constant speed. The difference in tension at the top and bottom would be

Moderate

A

6mg
B

5mg
C

2mg
D

mg

Solution

$t e n s i o n i n s t r i n g a t l o w e s t p o i n t T_{L} = \frac{m v^{2}}{r} + m g - - - (1) t e n s i o n i n s t r i n g a t h i g h e s t p o i n t T_{H} = \frac{m v^{2}}{r} - m g - - - (2) h e r e b o d y h a s c o n s \tan t s p e e d v d i f f e r e n c e i n t e n s i o n i s f r o m e q n (1) - e q n (2) T_{L} - T_{H} = 2 m g w h e r e m i s m a s s o f t h e b o d y, g i a c c e l e r a t i o n d u e t o g r a v i t y$

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